Algebraic Solver

Quadratic Equation Solver

Find the roots of any quadratic equation of the form $ax^2 + bx + c = 0$ with step-by-step formula derivations.

Enter Coefficients

Calculated Roots

x₁ = 3.00 x₂ = 2.00

Step-by-Step Derivation:

Discriminant (Δ) = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1 (Δ > 0, Two Real Roots) x = (-b ± √Δ) / 2a x = (5 ± 1) / 2 x₁ = 3.00, x₂ = 2.00

What is the Quadratic Equation Solver?

The Quadratic Equation Solver is a foundational algebra tool that calculates the "roots" (or x-intercepts) of a second-degree polynomial. It is essential for plotting parabolas and solving physics problems involving gravity and projectiles.

How It Works (Formula)

The tool uses the legendary Quadratic Formula. By analyzing the standard equation form $ax^2 + bx + c = 0$, it evaluates the discriminant ($b^2 - 4ac$) to determine if the parabola yields two real roots, one real root, or complex imaginary roots.

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

The universal quadratic formula used to solve for x.

How to Use It

Ensure your equation is organized in the $ax^2 + bx + c = 0$ format. Input the numerical coefficients for A, B, and C. The calculator will immediately output the two values of X where the curve crosses the axis.