Quadratic formula
x = ( −b ± √(b² − 4ac) ) ÷ 2a
For any equation ax² + bx + c = 0 (a ≠ 0). The discriminant b² − 4ac reveals the roots before you solve: positive → two distinct real roots, zero → one repeated real root, negative → two complex conjugate roots.
Solving quadratic equations
A quadratic equation has the form ax² + bx + c = 0. The quadratic formula, x = (−b ± √(b² − 4ac)) / 2a, solves any of them. The quantity under the root, the discriminant, determines whether the roots are real and distinct, real and repeated, or complex.
This tool also reports the parabola's vertex and the direction it opens, which is useful for graphing and optimization problems.