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Quadratic Equation Solver

Solve ax² + bx + c = 0 with the quadratic formula and discriminant.

Best for: Algebra and physics problems, projectile and optimisation questions, and anywhere a parabola models the situation.

Complete guide

Input

How it's calculated & sources
The Quadratic Equation Solver uses the standard, deterministic formula, so the same inputs always produce the same result. It runs entirely in your browser, so your inputs are never uploaded. Last reviewed June 2026.

Free & no sign-up · runs entirely in your browser. Results are estimates for general information, not professional advice — verify important decisions with a qualified expert. Last reviewed June 2026.

How it works

x = (−b ± √(b² − 4ac)) / 2a, for ax² + bx + c = 0.

Example

x² − 3x + 2 = 0 → x = 1, x = 2

Frequently asked questions

What does the discriminant tell me?+

If b²−4ac > 0 two real roots, = 0 one repeated root, < 0 two complex roots.

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Complete guide

Quick answers

Short, sourced answers to the questions people (and AI assistants) ask most.

What is Quadratic Equation Solver?
A quadratic equation solver finds the values of x that satisfy ax^2 + bx + c = 0 using the quadratic formula.
Why does Quadratic Equation Solver matter?
The roots are the x-values where the parabola crosses the x-axis (or, for a negative discriminant, a complex-conjugate pair).
How is Quadratic Equation Solver calculated?
It applies x = (-b plus or minus sqrt(b^2 - 4ac)) / 2a. The part under the root, b^2 - 4ac, is the discriminant: if it is positive there are two real roots, if zero there is one repeated root, and if negative there are two complex roots. Formula: x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a.
What are common quadratic equation solver mistakes?
Sign slips with b, especially when b is negative.
When should you use the Quadratic Equation Solver?
Algebra and physics problems, projectile and optimisation questions, and anywhere a parabola models the situation.

What is the Quadratic Equation Solver?

A quadratic equation solver finds the values of x that satisfy ax^2 + bx + c = 0 using the quadratic formula.

How the Quadratic Equation Solver works

It applies x = (-b plus or minus sqrt(b^2 - 4ac)) / 2a. The part under the root, b^2 - 4ac, is the discriminant: if it is positive there are two real roots, if zero there is one repeated root, and if negative there are two complex roots.

x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a

Key terms

Discriminant:
b^2 - 4ac; its sign reveals how many real roots exist.
Root:
A value of x that makes the equation equal zero.

Common mistakes to avoid

  • Sign slips with b, especially when b is negative.
  • Forgetting the plus-or-minus, which gives the second root.
  • Dividing by 2 instead of 2a.
  • Reporting no solution when the discriminant is negative — the roots are complex, not absent.

Keywords: quadratic, equation, roots.

Sources: Khan Academy — The quadratic formula

Reviewed by the Free Tools Galaxy editorial team · Updated June 2026 · Calculated privately in your browser.

Frequently asked questions

Is the Quadratic Equation Solver free to use?+

Yes. Every tool on Free Tools Galaxy is 100% free, runs in your browser and requires no signup.

How accurate is the Quadratic Equation Solver?+

Quadratic Equation Solver uses the standard quadratic equation solver formula in double-precision arithmetic, so the same inputs always produce the same result and you can verify any figure by hand. It is an educational estimate — real-world outcomes depend on your actual rates, rules and assumptions.

Do you store my inputs?+

No. The Quadratic Equation Solver runs entirely in your browser. Nothing is uploaded or saved to a server.

Can I use the Quadratic Equation Solver on mobile?+

Yes — the interface is fully responsive and works on phones, tablets and desktops.

What are common mistakes to avoid?+

The most frequent mistake is mixing units. Double-check your inputs use a single, consistent unit before clicking Calculate.

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Solve ax² + bx + c = 0 with the quadratic formula and discriminant.

Try it: https://freetoolsgalaxy.com/tools/quadratic-equation-solver
Quora answer
The fastest way is to use a free in-browser quadratic equation solver: https://freetoolsgalaxy.com/tools/quadratic-equation-solver. Solve ax² + bx + c = 0 with the quadratic formula and discriminant.

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