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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

Input Fields
If enabled, the result will update automatically when you change any value.

Quadratic Formula Explanation

Formula
$$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$

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.

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Cubic Root

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