Solve quadratic equations (ax² + bx + c = 0)

Solve a quadratic equation and report real or complex roots from its discriminant.

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ToolQuadratic Solver
Input
Output
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How it works

The discriminant b²−4ac determines the case: positive gives two real roots, zero gives a repeated root, and negative gives a conjugate complex pair. Roots use the quadratic formula and are rounded for display.

  • a must be nonzero.
  • Coefficients are parsed from the supplied three-number expression.

Worked example

Solve x^2 - 5x + 6 = 0
Find the roots of x^2 - 5x + 6 = 0
Input
											1, -5, 6
Output
												Equation: 1x² + -5x + 6 = 0
Discriminant: 1
Two real roots:
x₁ = 3
x₂ = 2

When to use this

Math lessons find parabola intercepts, projectile equations find times, and engineering models test real solutions.

Edge cases

  • a = 0 is rejected as a linear equation.
  • A negative discriminant has complex rather than real roots.
  • Very large coefficients can lose precision when squared.