Quadratic Equation Solver: Free Calculator with Steps
Solve quadratic equations by the formula, by factoring or by completing the square. Free, with no sign-up.
Use ^ for powers and brackets for groups, such as (x - 1)(x + 2) = 4. Try an example:
How to Use the Quadratic Equation Solver
1
Pick a Tab
Choose the quadratic formula, factoring or completing the square.
2
Type Your Equation
Use ^ for powers, such as x^2 – 5x + 6 = 0.
3
Read the Steps
See each step, both roots and the discriminant.
What It Can Solve
x²
Real Roots
Equations with two solutions or one repeated solution.
i
Complex Roots
Equations with a negative discriminant, shown with i.
( )( )
Any Form
Brackets and terms on both sides, such as (x − 1)(x + 2) = 4.
Worked Example: x² − 5x + 6 = 0
- Identify a, b and c: a = 1, b = −5, c = 6
- Find the discriminant: (−5)² − 4 × 1 × 6 = 1
- Apply the formula: x = (5 ± 1) ÷ 2, so x = 3 or x = 2
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Frequently Asked Questions
Is the Quadratic Equation Solver free?
Yes. It is free and needs no sign-up.
What is the discriminant?
It is b² − 4ac. Positive means two real roots, zero means one repeated root, and negative means two complex roots.
Which method should I use?
Use factoring for simple whole-number roots, the formula for any quadratic, and completing the square to see how the formula is built.
Why does it say there are no real roots?
When the discriminant is negative, the parabola never crosses the x-axis, so the solutions are complex numbers written with i.
What if my equation has no x squared term?
Use the Linear Equation Solver. This page only solves equations that work out as ax² + bx + c = 0.
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