Quadratic Equation Solver

Solve ax² + bx + c = 0 with real or complex roots, discriminant, vertex, factored form and steps.

How do you solve a quadratic equation?

Use the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. The discriminant b² − 4ac tells you the type of roots: positive gives two real roots, zero gives one repeated root, and negative gives two complex roots.

Example

x² − 3x + 2 = 0 → a = 1, b = −3, c = 2 → discriminant = 9 − 8 = 1 → x = (3 ± 1) / 2 → x = 1 or x = 2, factored form (x − 1)(x − 2).

The vertex (−b/2a, c − b²/4a) is the turning point of the parabola.

Frequently asked questions

What if a = 0?

The equation is linear (bx + c = 0) and the tool solves x = −c/b.

What are complex roots?

Solutions with an imaginary part (i = √−1), which appear when the parabola never crosses the x-axis.

Can I enter decimals?

Yes, any real numbers.