AI Math 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 solver flags extraneous solutions in rational equations and notes when the discriminant is negative (complex roots).
- 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. The solver handles polynomials up to degree 4, returning both real and complex roots. For cubics like x³ − 6x² + 11x − 6 = 0, you get all three roots with the factorization shown.
Systems of equations. 2×2 and 3×3 linear systems are solved using both substitution and elimination methods — every step shown. The elimination output follows the TI-84's rref() matrix method. Need the matrix approach? Use the matrix calculator for Gaussian elimination.
Trigonometric equations like sin(x) = 0.5. The solver accounts for periodicity and returns all solutions within the specified interval.
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, quadratic, cubic, and quartic equations — all with step-by-step working
- Systems of equations — 2×2 and 3×3 with substitution and elimination shown
- Trigonometric equations — sine, cosine, tangent with full periodicity handling
- Polynomial factoring — real and complex factors with verification step
- Inequality solver — linear and quadratic with interval notation output
- Natural language input — type "solve 3x + 7 = 22" exactly like you would write it
Equation Solver FAQ
Is this equation solver free?
Yes, completely free. No signup, no download, no usage limits. Every equation type — linear, quadratic, cubic, quartic, systems, trigonometric — works with full step-by-step solutions at no cost. Most free solvers either hide the steps behind a paywall or show only the final answer. Ours shows everything.
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 system solver handles 2×2 and 3×3 linear systems using both substitution and elimination methods, with every step shown. The elimination output is consistent with the TI-84's rref() matrix method — results match to machine precision. For larger systems, use the matrix calculator with the RREF function.
How accurate are the solutions?
Solutions follow standard textbook methods, and the solver cross-checks every answer by substituting it back into the original equation. A built-in local math engine keeps results coming even when the AI explanation 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 is free to use with no limits. WolframAlpha and Symbolab both charge for step-by-step solutions; this one is free.
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.
Page last updated: August 4, 2026
Miqdad Qaisrani
Educational Software Engineer & 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.