Free Online Equation Solver
Free online equation solver — solve linear, quadratic, cubic, quartic, and systems of equations with step-by-step solutions. Type naturally like "solve 3x + 7 = 22" and see every algebraic step. No download, no sign-up.
Everything You Can Do With This Equation Solver
The Solver That Shows Its Work
This is a free AI-powered equation solver that shows every algebraic step — not just the final answer. Type an equation, hit solve, and see the full working: factoring, substitution, quadratic formula, elimination. This solver handles the same problem types as a TI-84 Plus CE but shows the working, which is the difference between copying and actually learning the method.
Using the Solver: A Five-Step Walkthrough
- Type your equation. Write it like you would on paper: 3x + 7 = 22 or x^2 + 5x + 6 = 0. You can use natural language — "solve 2x^2 - 8x + 6 = 0" works just as well as typing the equation alone.
- Click Solve. The AI engine processes your equation and returns a step-by-step solution.
- Read through each step. For linear equations, you will see the variable isolated step by step. For quadratics, you get the discriminant, the quadratic formula substitution, and both roots.
- Check for edge cases. The local quadratic solver states when the discriminant is negative and the roots are complex, which is one of the most common places to lose marks.
- Try a variation. Change a number and solve again. Seeing how the steps change when you modify the equation builds understanding faster than reading a textbook.
What Types of Equations Can This Solver Handle?
Linear equations like 3x + 7 = 22. The solver isolates the variable step by step and returns x = 5. These are the foundation of Algebra 1 — if you are just starting out, begin here.
Quadratic equations like x² + 5x + 6 = 0. The solver shows the discriminant (b² − 4ac), applies the quadratic formula, and returns both roots (x = −2 and x = −3 in this case). You also get the factored form (x + 2)(x + 3), vertex coordinates, and axis of symmetry. For a full walkthrough of quadratic solving by hand, see our TI-84 quadratic formula tutorial.
Cubic and quartic equations. Polynomials above degree 2 are routed to the cloud AI engine rather than the built-in local solver. Type a cubic like x³ − 6x² + 11x − 6 = 0 and the AI explanation works through the roots step by step. Because this path is AI-generated rather than computed locally, treat the working as a study aid and check it against your own method.
Systems of equations. The local solver handles 2×2 linear systems. Systems with three or more variables are routed to the cloud AI engine. For a deterministic matrix approach that uses the same rref() method as the TI-84, use the matrix calculator.
Trigonometric equations like sin(x) = 0.5. These are handled by the cloud AI engine, not the local solver. State the interval you want (for example, 0° to 360°) and the AI explanation will list the solutions it finds in that range.
How Do I Solve a Quadratic Equation Step by Step?
Here is exactly what you will see when you type x² − 5x + 6 = 0:
Step 1: Identify coefficients: a = 1, b = −5, c = 6
Step 2: Discriminant: b² − 4ac = (−5)² − 4(1)(6) = 25 − 24 = 1
Step 3: Since discriminant > 0, there are two real roots.
Step 4: Apply quadratic formula: x = [−b ± √(b²−4ac)] / 2a
Step 5: x = [5 ± √1] / 2 = [5 ± 1] / 2
Step 6: x₁ = (5 + 1) / 2 = 3, x₂ = (5 − 1) / 2 = 2
Step 7: Factored form: (x − 3)(x − 2) = 0
Vertex: (2.5, −0.25) | Axis of symmetry: x = 2.5
Compare this to a TI-84 — the handheld gives you x = 2 and x = 3 but does not show the discriminant, the factored form, or the vertex. This solver shows everything in one view. For a keystroke-by-keystroke guide to solving quadratics on the physical calculator, see our TI-84 graphing calculator guide.
A Look at Every Solver Capability
- Linear and quadratic equations — solved by the local engine with step-by-step working
- Simple derivatives and polynomial factoring — solved locally
- Systems of equations — 2×2 solved locally; 3×3 and larger handled by the AI engine
- Cubic, quartic, trigonometric, and inequality problems — handled by the AI engine, not the local solver
- Local linear and factoring results are checked by substituting the answer back into the original expression
- Natural language input — type "solve 3x + 7 = 22" exactly like you would write it
Advanced problem types depend on the AI service being reachable. When it is not, the local engine still works on the equation types listed above.
Equation Solver FAQ
Is this equation solver free?
Yes, completely free. No signup, no download. AI-assisted solves are capped by a small daily limit; once you reach it, the local engine still solves linear equations, quadratics, simple derivatives, factoring, and 2×2 systems with step-by-step working. Nothing is hidden behind a paywall.
Does it show every step of the solution?
Yes. For linear equations, you see the variable isolated term by term. For quadratics, you see the discriminant calculation, the quadratic formula substitution, simplification, both roots, the factored form, and the vertex coordinates. Teachers tell us this level of detail is what turns a "cheating tool" into a study aid — students can follow the logic from start to finish.
Can it solve systems of equations?
Yes. The built-in local solver handles 2×2 linear systems. Systems with three or more variables are passed to the cloud AI engine, so their accuracy depends on the AI rather than on a local computation. For a deterministic result you can check by hand, use the matrix calculator with the RREF function.
How accurate are the solutions?
The local engine follows standard textbook methods for linear equations, quadratics, simple derivatives, factoring, and 2×2 systems, and it checks its linear and factoring results by substituting the answer back into the original expression. AI-generated explanations for advanced problems should be verified against your own working. The local engine also keeps working when the AI service is temporarily unavailable.
Can this replace my TI-84 for exams?
This solver is a learning tool, not an exam substitute. Use it to check homework, understand steps you missed, and practice problem-solving. For actual exams, you will need your physical TI-84 — but practicing with this solver will make you faster and more confident on test day.
Can it solve trigonometric equations?
Yes. The solver handles sine, cosine, and tangent equations with full periodicity tracking. Type sin(x) = 0.5 and it returns all solutions within the specified interval. This is useful for Precalculus and Trigonometry homework where finding all angle solutions matters.
What makes this different from WolframAlpha or Symbolab?
This solver prioritizes readable, line-by-line working that matches how a teacher writes on the board — not dense mathematical notation aimed at experts. It costs nothing and requires no account; AI-assisted solves are subject to a small daily limit, after which the local engine takes over. WolframAlpha and Symbolab both charge for step-by-step solutions; this one does not.
To dig deeper, our TI-84 quadratic formula tutorial walks through the same methods keystroke by keystroke on a handheld calculator. The graphing calculator plots any equation you solve here, and the matrix calculator handles larger systems through RREF. For the underlying algebra, Khan Academy's algebra course and Purplemath walk through the same methods in depth.
Page last updated: October 13, 2026
Miqdad Qaisrani
Creator of Calc84
Miqdad is a full-stack engineer and cybersecurity student specializing in educational technology (EdTech). He engineered this AI math solver to ensure students receive step-by-step, textbook-aligned algebraic explanations, eliminating the paywalls that traditionally restrict access to detailed mathematical working.