Quadratic Equation Solver
Solve ax² + bx + c = 0 with the quadratic formula. Shows the discriminant, both roots (real or complex), and the full working.
Coefficients
ax² + bx + c = 0
Fill in a, b, c and press Solve.
About this calculator
Enter coefficients a, b, c for the quadratic ax² + bx + c = 0. The solver uses the discriminant to determine whether the roots are two real, one repeated, or a complex-conjugate pair, then applies the quadratic formula.
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How the quadratic formula works
The quadratic formula x = (−b ± √(b² − 4ac)) / 2a solves any equation of the form ax² + bx + c = 0. The discriminant Δ = b² − 4ac determines the nature of the roots: Δ > 0 gives two distinct real roots, Δ = 0 gives one repeated real root (the vertex touches the x-axis), and Δ < 0 gives a complex-conjugate pair (no real roots).