Solve quadratic equations and get real or complex roots instantly.
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. Quadratics appear in algebra, physics, finance, and geometry. The solutions (roots) are the x-values where the parabola crosses the x-axis. The discriminant (b² − 4ac) tells you the type of roots you will get.
The standard quadratic formula is x = (-b ± √(b² − 4ac)) / (2a). If the discriminant is positive, the equation has two real roots. If it is zero, there is one repeated real root. If it is negative, the equation has two complex conjugate roots.
To use the calculator, enter the coefficients a, b, and c and click Calculate. The tool computes the discriminant and displays the roots. It supports decimal inputs and shows complex roots in a + bi form when needed.
If a is zero, the equation becomes linear (bx + c = 0). The calculator detects this case automatically and returns the linear solution or reports no or infinite solutions when appropriate.
For a = 1, b = -3, c = 2, the equation is x² − 3x + 2 = 0 and the roots are x1 = 2 and x2 = 1. For a = 1, b = 2, c = 5, the discriminant is -16, so the roots are complex: x = -1 ± 2i.