Math Lab · Calculator
Quadratic Equation Solver
See how the discriminant determines the roots and inspect the key features of the parabola.
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Verify this calculatorMaintained
See what the result uses—and what it cannot know.
Sumvoro calculates deterministically from the visible inputs. It does not invent lender terms, local rules, market values, medical facts, or professional judgments.
- 1 · InputsCheck every entered value against the latest statement, quote, measurement, or official source.
- 2 · Formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant Δ = b² − 4ac determines the root type. - 3 · SensitivityUse Insights to run a lower and higher case. If the conclusion changes easily, collect better information or leave more margin.
- 4 · ScopeThis tool is maintained and covered by automated calculation tests. Provider timing, rounding, and omitted facts can still change a real-world result.
Calculation receiptSV-2026104-1XL897O
- Formula release
- 2026.10-r4
- Release date
- October 10, 2026
- Review status
- Maintained
- Source review
- September 12, 2026
Optional readingLearn how this calculator works
How the quadratic equation solver works
Solve ax² + bx + c = 0 using the quadratic formula, discriminant, vertex, and real or complex roots.
Formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant Δ = b² − 4ac determines the root type.
Read our calculation methodology and limitations.
Example
For x² − 5x + 6 = 0, the discriminant is 1 and the roots are 2 and 3.
What affects the result
- A must be nonzero for a quadratic equation.
- A negative discriminant produces complex conjugate roots.
- The axis of symmetry is x = −b ÷ 2a.
Frequently asked questions
What does a negative discriminant mean?
There are no real roots; the two solutions contain the imaginary unit i.
Does this factor every quadratic?
It reports roots from the quadratic formula even when simple integer factoring is unavailable.