Quadratic Equation Calculator
Enter the coefficients a, b and c to solve a quadratic equation. VELNARO shows the discriminant, both roots (real or complex), and the vertex of the parabola.
Root x₁
3
Discriminant (Δ)
1
Two distinct real roots
Root x₂
2
Vertex
(2.5, -0.25)
Axis of symmetry
x = 2.5
How this was worked out
- Step 1Δ = b² − 4ac = -5² − 4 × 1 × 6 = 1
- Step 2x = (−b ± √Δ) ÷ 2a
- Step 3x₁ = 3, x₂ = 2
Formula
x = (−b ± √(b² − 4ac)) ÷ 2a
Example
Input
x² − 5x + 6 = 0
Result
x = 2 and x = 3
Frequently asked questions
The equation has no real roots; the calculator shows the two complex roots instead.
Then the equation is linear, not quadratic. Solve it as bx + c = 0.
The vertex is the turning point of the parabola, at x = −b ÷ 2a.
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