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HQ8T

Quadratic Equation Solver

Solve ax² + bx + c = 0 with steps and graph.

ax² + bx + c = 0

x² - 5x + 6 = 0

Roots
x₁ = 3, x₂ = 2
Two real roots
Discriminant (D)
1
Vertex
(2.5, -0.25)
Minimum point

Factored form: (x − 3)(x − 2)

Step by step

  1. x² - 5x + 6 = 0
  2. a = 1, b = -5, c = 6
  3. Discriminant D = b² − 4ac = (-5)² − 4 × 1 × 6 = 1
  4. D > 0, so there are two different real roots: x = (−b ± √D) / 2a
  5. √D = 1
  6. x₁ = (5 + 1) / 2 = 3
  7. x₂ = (5 − 1) / 2 = 2

How to use

  1. 1Enter the values of a, b and c from ax² + bx + c = 0.
  2. 2See the discriminant and the roots right away.
  3. 3Read the step-by-step working with the quadratic formula.
  4. 4Check the graph, vertex and factored form.

Frequently asked questions

What is the quadratic formula?

x = (−b ± √(b² − 4ac)) / 2a. The part under the root, b² − 4ac, is called the discriminant (D).

What does the discriminant tell me?

D > 0 means two different real roots, D = 0 means one repeated root, and D < 0 means no real roots (two complex roots).

Can a be zero?

No. With a = 0 the equation becomes linear (bx + c = 0), not quadratic.

What is the vertex?

The turning point of the parabola, at x = −b/2a. It is the minimum point when a > 0 and the maximum when a < 0.

Does it work with decimals and negative numbers?

Yes. Any real numbers work for a, b and c, and roots are shown up to 6 decimal places.

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