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Quadratic Equation Solver

How do I solve a quadratic equation?

Enter the three numbers of a quadratic equation and see its solutions, worked out step by step.

One Click Answers · Quadratic Equation Solver
oneclickanswers.com/quadratic-equation-solver · Printed
About this tool & how to use it

What it does

Enter a, b and c to solve a quadratic equation, with the discriminant, both roots, the vertex and the steps. A linear equation mode is included.

How to use it

  1. Write your equation as ax² + bx + c = 0 and enter a, b and c. For x² − 5x + 6 = 0 that is a = 1, b = −5 and c = 6. Use 0 for a term that is missing.
  2. Read the solutions in the sentence at the top, then the discriminant and the steps.
  3. See the factored form (when there is one), the vertex and which way the curve opens. Choose the linear option to solve ax + b = c instead.

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Assumptions

  • The equation must be in the form ax² + bx + c = 0, with everything moved to the left-hand side. For a quadratic, a cannot be 0.
  • Roots are shown to at most 6 decimal places. The factored form is shown only when a, b and c are whole numbers and the roots come out exactly.
  • Everything you enter is worked out in your browser and is never sent anywhere.

Printed from oneclickanswers.com. Results are estimates based on what was entered; see the assumptions above.

How we calculated this

The quadratic formula gives the solutions: x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the square root, b² − 4ac, is the discriminant.

If the discriminant is positive there are two real solutions, if it is zero there is one repeated solution, and if it is negative there are no real solutions: the two answers are complex numbers of the form p ± qi.

The vertex is the turning point of the curve, at x = −b ÷ 2a. The curve opens upward when a is positive and downward when a is negative.

For a linear equation the solution is x = (c − b) ÷ a. When a is 0 the x disappears: the equation is then either true for every x or true for none.

Formulas and details
  • x = (−b ± √(b² − 4ac)) ÷ 2a
  • Discriminant = b² − 4ac
  • Vertex x = −b ÷ 2a
  • Linear: x = (c − b) ÷ a

Assumptions

  • The equation must be in the form ax² + bx + c = 0, with everything moved to the left-hand side. For a quadratic, a cannot be 0.
  • Roots are shown to at most 6 decimal places. The factored form is shown only when a, b and c are whole numbers and the roots come out exactly.
  • Everything you enter is worked out in your browser and is never sent anywhere.

Example

Input: x² − 5x + 6 = 0

Result: x = 2 or x = 3. The discriminant is 1, the factored form is (x − 2)(x − 3), and the vertex is (2.5, −0.25).

Questions

What is the discriminant?

It is b² − 4ac. It tells you what kind of solutions to expect before you work them out: positive means two real solutions, zero means one, and negative means none that are real numbers.

What if my equation is not equal to 0?

Move everything to one side first. For x² + 3x = 10, subtract 10 from both sides to get x² + 3x − 10 = 0, then enter a = 1, b = 3 and c = −10.

What does it mean when the answers have an "i"?

The curve never touches the x-axis, so no real number solves the equation. The two solutions are complex numbers, written with i, where i is the square root of −1.

Last reviewed 2026-10-07. Report an incorrect result

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