Quadratic and Linear Equation Solver
Enter the coefficients and get the discriminant, roots and vertex using the quadratic formula.
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| Discriminant (Δ = b² − 4ac) | 1 |
| x₁ | 3 |
| x₂ | 2 |
| Vertex of the parabola | (2.5; -0.25) |
Two real roots · Quadratic formula: x = (−b ± √Δ) ÷ 2a
Quick answer: To solve a quadratic equation, write it as ax² + bx + c = 0 and enter a, b and c: the solver shows the discriminant (Δ = b² − 4ac), the roots from the quadratic formula and the vertex of the parabola. If Δ is negative, you get the complex roots. For linear equations, use ax + b = 0.
How to do it in 3 steps
- 1Choose linear or quadratic.
- 2Enter the coefficients.
- 3See the discriminant, roots and vertex.
Why use Pronto Arquivo
Quadratic formula, automatic
Discriminant and both roots instantly.
Complex roots
When Δ < 0, shows the result with i.
Vertex
Maximum or minimum point of the parabola.
Linear too
ax + b = 0 in one click.
Guides
Example
x² − 5x + 6 = 0: a = 1, b = −5, c = 6. Δ = 25 − 24 = 1, so x = (5 ± 1) ÷ 2: x₁ = 3 and x₂ = 2.
Frequently asked questions
How do I solve a quadratic equation?
Compute Δ = b² − 4ac, then x = (−b ± √Δ) ÷ 2a.
What does a negative discriminant mean?
There are no real roots; the roots are complex.
What if a is zero?
It isn't a quadratic equation; use linear mode.
How do I find the vertex?
x = −b ÷ 2a and y = −Δ ÷ 4a.
