Quadratic Equation Solver
Solve ax² + bx + c = 0 with real or complex roots, the discriminant and the vertex of the parabola.
How to use the Quadratic Equation Solver
- Enter or select: a, b, c.
- The results (Discriminant Δ, Root x₁, Root x₂, Vertex (h, k), Nature of roots) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- x = (−b ± √(b² − 4ac)) / 2a
- Δ = b² − 4ac
About this tool
If Δ > 0 there are two real roots, Δ = 0 gives one repeated root and Δ < 0 gives a pair of complex conjugate roots. The solver uses a numerically stable form to avoid cancellation errors.