Quadratic Formula Calculator
Solve any quadratic equation ax² + bx + c = 0. Find both roots instantly — real or complex — with the discriminant shown.
How to calculate Quadratic Formula
The quadratic formula solves any equation of the form ax² + bx + c = 0, where a ≠ 0. It is one of the most important results in algebra, taught in schools worldwide as a universal method for finding the roots of a parabola.
The formula is x = (−b ± √(b² − 4ac)) / 2a. The expression under the square root, b² − 4ac, is called the discriminant and determines the nature of the roots.
If the discriminant is positive, there are two distinct real roots — the parabola crosses the x-axis twice. If it is zero, there is exactly one real root (a double root) — the parabola touches the x-axis at its vertex. If it is negative, there are two complex roots — the parabola does not cross the x-axis at all.
For example, x² − 5x + 6 = 0 has roots x = 3 and x = 2, since (5 ± √(25−24)) / 2 = (5 ± 1) / 2.
Quadratic equations model projectile motion, the shape of satellite dishes, profit optimisation in business, and the paths of planets. This calculator shows both roots and the discriminant value.