📐 Quadratic Equation Calculator

Solving Quadratic Equations

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a ≠ 0. The solutions (roots) are found using the quadratic formula: x = (-b ± √(b²-4ac)) / 2a.

The Discriminant

• Δ > 0: Two distinct real roots — the parabola crosses the x-axis at two points.
• Δ = 0: One repeated (double) root — the parabola touches the x-axis at one point.
• Δ < 0: Two complex conjugate roots — the parabola doesn't cross the x-axis.

Quadratic equations appear frequently in physics (projectile motion), engineering (optimization), finance (break-even analysis), and many other fields.