Quadratic equation solver
Enter a, b and c of ax² + bx + c = 0. We find the discriminant and the solutions, even complex ones.
Result
2Solution 1
- Solution 2
- 3
- Discriminant Δ
- 1
- Vertex: x
- 2.5
- Vertex: y
- -0.25
Inputs
- a (in front of x²)
- 1
- b (in front of x)
- -5
- c (the plain number)
- 6
How it is calculated
Δ = b² − 4ac.
Result
Solution 1
- Solution 2
- 3
- Discriminant Δ
- 1
- Vertex: x
- 2.5
How it is calculated
- Δ = b² − 4ac.
- If Δ > 0: x = (−b ± √Δ) ÷ 2a, two solutions.
- If Δ = 0: one solution x = −b ÷ 2a.
- If Δ < 0: x = −b ÷ 2a ± i × √(−Δ) ÷ 2a.
- If a = 0: x = −c ÷ b.
Example
x² − 5x + 6 = 0: Δ = 25 − 24 = 1, so x = 2 or x = 3.
Good to know
- Results are rounded to 6 decimal places.
- If a = b = 0 there is no solution (c ≠ 0) or every number works (c = 0).
Frequently asked questions
What is this tool used for?
Enter a, b and c of ax² + bx + c = 0. We find the discriminant and the solutions, even complex ones.
How is the result calculated?
Δ = b² − 4ac.
What should I check before using the result?
Results are rounded to 6 decimal places.