Quadratic Equation Solver
Solve ax² + bx + c = 0 for any values of a, b and c. See both roots, the discriminant, step-by-step working and complex roots when the discriminant is negative.
The Quadratic Formula
Every quadratic equation ax² + bx + c = 0 can be solved using the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The term under the square root — b² − 4ac — is called the discriminant (Δ). Its sign tells you immediately how many real solutions exist: positive = two distinct real roots, zero = one repeated real root, negative = two complex conjugate roots.
What the Discriminant Means
The discriminant is the most important single piece of information about a quadratic. Δ > 0 means the parabola crosses the x-axis at two points. Δ = 0 means it touches the x-axis at exactly one point (the vertex is on the axis). Δ < 0 means the parabola never crosses the x-axis — solutions exist only in complex numbers.