About Quadratic Equation Solver
Solve any quadratic equation of the form ax² + bx + c = 0. Enter the coefficients and get the roots (real or complex), the discriminant, the vertex, and clear step-by-step working using the quadratic formula.
How to Use
- Enter the coefficients a, b, and c.
- The roots update instantly.
- Read the discriminant and the nature of the roots.
- Follow the step-by-step working to see how it's solved.
Why Use This Tool?
- Accurate — built on precise, well-tested mathematical formulas.
- Instant — all calculations happen client-side for zero latency.
- Private — no data is sent to any server; your information stays on your device.
- Free — no sign-up, no limits, no hidden costs.
Frequently Asked Questions
What is the quadratic formula?
For ax² + bx + c = 0, the solutions are x = (−b ± √(b² − 4ac)) / 2a. The part under the square root, b² − 4ac, is called the discriminant.
What does the discriminant tell me?
It reveals the nature of the roots: if b²−4ac > 0 there are two distinct real roots, if it equals 0 there is one repeated real root, and if it is negative the two roots are complex conjugates.
Can it solve equations with no real solution?
Yes. When the discriminant is negative the tool gives the two complex roots in the form p ± qi, instead of just saying 'no solution'.
What if a = 0?
Then it isn't a quadratic — it's linear (bx + c = 0). The tool detects this and gives the single linear solution x = −c/b instead.