TI 84 Quadratic Formula: How to Solve ax² + bx + c = 0

By Miqdad Qaisrani | Updated July 16, 2026

Learn how to solve quadratic equations on your TI-84 calculator using the quadratic formula. This guide covers step-by-step instructions, worked examples, and practical tips for the TI-84 quadratic formula method. Master solving ax² + bx + c = 0 on your TI-84 calculator online or physical device.

Quick Answer: Store coefficients a, b, c in A, B, C using STO→. Enter (-B+√(B²-4AC))/(2A) and (-B-√(B²-4AC))/(2A) for roots. Discriminant positive: 2 real solutions; zero: 1; negative: none.

The Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

Use this formula to find the roots of ax² + bx + c = 0

Understanding the Quadratic Formula

A quadratic equation is any equation in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The quadratic formula gives you the values of x where the parabola crosses the x-axis (the roots or solutions of the equation). This formula works for every quadratic equation, whether the solutions are real numbers or complex numbers.

The TI-84 calculator can solve quadratic equations using this formula quickly and accurately. While there is no dedicated "quadratic formula" button, you can enter the formula directly and get precise results. Use our free online TI-84 calculator as an alternative that works in your browser without any downloads.

The quadratic formula is derived from the method of completing the square. It has been a cornerstone of algebra for centuries and appears in mathematics curricula worldwide. Learning to apply it efficiently on your TI-84 will save you valuable time during exams and homework.

How to Solve Quadratic Equations on Your TI-84

Identify Your Coefficients

Look at your equation ax² + bx + c = 0 and identify the values of a, b, and c. For example, in 2x² - 4x - 6 = 0, the coefficients are a = 2, b = -4, and c = -6. Write these down before you start entering them into your calculator.

Store Values in Memory

For easier calculation, store the coefficients as variables: type the value for a, press STO→, then press ALPHA A. Repeat for b (STO→ ALPHA B) and c (STO→ ALPHA C). This lets you use A, B, and C directly in the formula instead of re-entering numbers each time.

Calculate the First Root

Enter the formula: (-B+√(B²-4AC))/(2A) then press ENTER. Use the square root key (√) found by pressing 2nd then x². Make sure to include all parentheses exactly as shown — missing parentheses are a common source of errors on the TI-84.

Calculate the Second Root

Press 2nd then ENTER (ENTRY) to recall the previous calculation. Use the left arrow key to move the cursor to the + sign, change it to -, and press ENTER. This gives you the second root without retyping the entire formula.

Example: Solve 2x² - 4x - 6 = 0

Here, a = 2, b = -4, c = -6

First root: (-(-4)+√((-4)²-4*2*(-6)))/(2*2)

(4+√(16+48))/4
Ans = 3

Second root: (-(-4)-√((-4)²-4*2*(-6)))/(2*2)

(4-√(64))/4
Ans = -1

Solution: x = 3 or x = -1

The parabola y = 2x² - 4x - 6 crosses the x-axis at x = 3 and x = -1. You can verify this by graphing the equation and using the CALC menu to find the zeros.

Example: Solve x² + 5x + 6 = 0

Here, a = 1, b = 5, c = 6

First root: (-5+√(5²-4*1*6))/(2*1)

(-5+√(25-24))/2
Ans = -2

Second root: (-5-√(5²-4*1*6))/(2*1)

(-5-√(1))/2
Ans = -3

Solution: x = -2 or x = -3. Both roots are negative because the coefficients b and c are both positive.

Understanding the Discriminant

What is the Discriminant?

The discriminant is the expression under the square root: b² - 4ac. Its value determines how many real solutions a quadratic equation has. Calculating the discriminant first on your TI-84 is a good practice because it tells you what to expect before computing the full formula.

b² - 4ac > 0: Two distinct real solutions. The parabola crosses the x-axis at two points.
b² - 4ac = 0: One real solution (a repeated root). The parabola touches the x-axis at exactly one point (the vertex).
b² - 4ac < 0: No real solutions. The parabola does not cross the x-axis. The solutions are complex numbers involving i.

On your TI-84, you can compute the discriminant separately by entering B² - 4AC and pressing ENTER before applying the full quadratic formula.

Tips for Using the Quadratic Formula

Watch Your Signs

If b or c is negative, use parentheses when entering values. Type (-4) instead of just -4 when substituting to avoid sign errors.

Use 2nd + ENTER

Press 2nd then ENTER to recall your last entry. Just change the + to - for the second root to save time and avoid retyping errors.

Store Variables First

Store a, b, and c in variables A, B, C using STO→. Then use A, B, C in your formula to keep your workspace clean.

Check with Graphing

Graph the quadratic using Y= and press CALC (2nd TRACE) then select "zero" to verify your calculated roots.

Common Mistakes to Avoid

When using the TI-84 quadratic formula method, watch out for these frequent errors:

Forgetting parentheses around negative values: Always wrap negative coefficients in parentheses. Enter (-4) not -4.
Missing the denominator parentheses: The entire expression (-b ± √(b² - 4ac)) must be divided by (2a). Forgetting outer parentheses gives wrong results.
Confusing the ± sign: You must run the formula twice — once with + and once with -. The calculator cannot do both at once automatically.
Using the wrong variable names: If you stored values in A, B, and C but then type lowercase a, b, c, the TI-84 will use whatever values those variables currently hold.
Not checking the discriminant first: Computing b² - 4ac first helps you know whether real solutions exist before entering the full formula.

Alternative Methods on TI-84

Program a Solver: Write a TI-BASIC program that prompts for a, b, c and displays both roots automatically
PolySmlt App: Use the Polynomial Root Finder application (pre-installed on many TI-84 Plus CE models)
Graph and Trace: Graph Y1 = ax²+bx+c, then use CALC → zero to find x-intercepts visually
Table Feature: Use the TABLE (2nd GRAPH) to scan for where Y = 0
Equation Solver: Use the numeric solver (MATH → Solver) for equations rearranged to equal zero

Practice Problems

Try solving these quadratic equations on your TI-84 to build confidence with the quadratic formula:

x² + 7x + 12 = 0 (Answer: x = -3, x = -4)
3x² - 11x + 6 = 0 (Answer: x = 3, x = 2/3)
4x² + 4x + 1 = 0 (Answer: x = -0.5, repeated root)
2x² + 3x + 5 = 0 (Answer: no real solutions, discriminant is negative)
x² - 10x + 25 = 0 (Answer: x = 5, repeated root)

For each problem, first compute the discriminant (b² - 4ac) to predict how many solutions exist, then use the full formula to find them. Need extra practice? Khan Academy offers free quadratic formula lessons with video explanations and additional exercises.

Ready to practice on the real interface? Open our TI-84 graphing calculator online guide for the full keypad, or install the free TI-84 emulator for Android to solve quadratics on your phone.

Page last updated: July 22, 2026

Miqdad Qaisrani

Full Stack AI Engineer & Creator of Calc84

Miqdad built Calc84's graphing calculator to give students a free, faithful TI-84 emulator. He's a full-stack engineer focused on browser-based math tools that work offline.

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