Quadratic Equation Solver interactive tool
Equation form:
ax² + bx + c = 0
Δ = b² − 4ac determines whether the roots are real and distinct, real and repeated, or complex.
Worked steps
Δ = b² − 4ac = (-3)² − 4(1)(2) = 1.0000
x = (−b ± √Δ) ÷ 2a
The positive discriminant gives two distinct real roots.
What Is Quadratic Equation Solver?
A quadratic equation solver is a focused algebra tool that finds the roots (solutions) of equations in the form ax² + bx + c = 0. These equations appear everywhere in school math, physics word problems, and optimization tasks.
How the Quadratic Formula Works
The standard way to solve any quadratic is to apply the quadratic formula:
x = (−b ± √(b² − 4ac)) / (2a)
The expression under the square root, b² − 4ac, is called the discriminant. It tells you how many real roots your quadratic has and whether you will see complex numbers.
- Δ > 0 → two distinct real roots.
- Δ = 0 → one repeated real root.
- Δ < 0 → two complex conjugate roots.
Worked Quadratic Formula Example
For x² − 5x + 6 = 0, use a = 1, b = −5, and c = 6. The discriminant is 1, so the roots are x = 2 and x = 3.
Why Use an Online Quadratic Equation Solver?
This quadratic equation calculator is useful for checking algebra homework, exploring how changing coefficients affects the roots, or solving word problems that reduce to ax² + bx + c = 0. Because the calculation runs in your browser, you can experiment with negative, fractional, or large coefficients without sending the equation to a calculation service.
How To Use the Quadratic Equation Solver
- Enter the coefficients a, b, and c for your quadratic equation in the form ax² + bx + c = 0.
- Check that the value of a is non-zero so the equation is truly quadratic.
- Review the discriminant value to see whether the equation has two real roots, one repeated real root, or two complex roots.
- Follow the displayed discriminant and formula substitution, then read the calculated roots.
- Use the Example button to load a sample quadratic, or Reset to clear all three coefficient fields.
Quadratic formula, roots, and discriminant
Use this quadratic equation solver for ax² + bx + c = 0 when you need the roots, discriminant, and formula substitution. It handles real and complex roots and is useful for checking a quadratic formula setup.
Need the formula or convention behind this result? Read the calculator methods and assumptions.