How it works

Our Quadratic Equation Solver helps you find the roots (solutions) for any quadratic equation in the standard form ax² + bx + c = 0. Just enter the coefficients a, b, and c, and we'll show you the real or complex solutions, the discriminant, and even the vertex.

The Formula

The quadratic formula is given by:
x = [-b ± √(b² - 4ac)] / 2a Where:
a, b, c are coefficients
x represents the roots (solutions)

Worked Example

1. Example: Solve x² + 5x + 6 = 0

   For the equation x² + 5x + 6 = 0, we have a=1, b=5, and c=6. Using the quadratic formula: x = [-5 ± √(5² - 4*1*6)] / (2*1) x = [-5 ± √(25 - 24)] / 2 x = [-5 ± √1] / 2 x1 = (-5 + 1) / 2 = -4 / 2 = -2 x2 = (-5 - 1) / 2 = -6 / 2 = -3 The roots are x = -2 and x = -3.

Tips, Assumptions & Limitations

• Ensure your equation is in the standard form ax² + bx + c = 0 before entering coefficients.
• If a coefficient is negative, include the minus sign (e.g., -5 for b).
• If a term is missing, its coefficient is 0 (e.g., for x² + 4 = 0, b=0).
• The discriminant (b² - 4ac) tells you about the nature of the roots: positive means two real roots, zero means one real root, negative means two complex roots.