Quadratic Equation Solver

How to solve a quadratic equation

1. Write your equation as ax² + bx + c = 0 and enter a, b and c.
2. The roots appear, real or complex.
3. The discriminant, the vertex of the parabola and the factored form are shown below them.

Frequently asked questions

What is the quadratic formula?

x = (−b ± √(b² − 4ac)) ÷ 2a. For x² − 5x + 6 = 0 it gives x = 3 and x = 2.

What does the discriminant tell me?

b² − 4ac decides the roots: above zero gives two real roots, exactly zero one repeated root, and below zero two complex roots.

How do I find the vertex?

The turning point is at x = −b ÷ 2a, and its y value is c − b² ÷ 4a.

Are my numbers sent anywhere?

No. Everything is worked out in your browser and nothing is stored or uploaded.