Quadratic Equation Solver
This calculator helps you quickly and accurately solve any quadratic equation of the form $$ax² + bx + c = 0$$. Ideal for students, teachers, and professionals, it uses the quadratic formula to find real or complex roots based on the discriminant.
Quadratic Equation Solver
Quadratic Formula Explanation
$$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$
Explanation:
This formula solves the quadratic equation $$ax² + bx + c = 0$$. The term under the square root, $$b² – 4ac$$, is called the discriminant (D).
- If $$D > 0$$: two real and distinct roots.
- If $$D = 0$$: one real root (a double root).
- If $$D < 0$$: two complex conjugate roots.
Quadratic equations commonly appear in algebra, physics, engineering, and economics. This calculator instantly computes roots using the well-known quadratic formula. Just enter coefficients $$a$$, $$b$$, and $$c$$, and it will handle the rest—including complex solutions. It’s especially helpful for checking homework, solving real-world problems, or automating repetitive tasks.