Free Quadratic Equation Solver — Solve ax² + bx + c = 0 Online
The Quadratic Equation Solver helps you solve any quadratic equation in the form ax² + bx + c = 0. Simply enter the coefficients a, b, and c, and the calculator finds both real and complex roots instantly.
The quadratic formula x = (-b ± √(b²-4ac)) / 2a is one of the most fundamental formulas in algebra. Our solver applies this formula and shows you the discriminant, roots, vertex, and step-by-step solution.
The discriminant (Δ = b² - 4ac) determines the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one repeated root; if Δ < 0, there are two complex conjugate roots.
This tool is perfect for students learning algebra, teachers preparing examples, and anyone who needs quick quadratic equation solutions.