Math

Quadratic Equation Solver

Solve ax² + bx + c = 0 with real or complex roots.

Last validated: 2026-02-14

Quadratic Equation Solver finds roots of `ax^2 + bx + c = 0`, including complex solutions when needed. It is useful for algebra classes and quick model equation checks. The tool handles discriminant logic automatically. Use it to verify equation-solving steps.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Quadratic Inputs

Solve equations of the form ax² + bx + c = 0.

Roots

Type: Real

Discriminant: 1.0000

Root 1: 2.0

Root 2: 1.0

How to use this tool

Enter coefficients a, b, and c.
Run the solver to compute roots.
Review discriminant and root type before interpreting results.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

A: 1.0
B: -3.0
C: 2.0
Root 1: 2.0
Root 2: 1.0
Equation type: real

Expected Outputs

A: 1
B: -3
C: 2
Discriminant: 1

Interpretation

A is 1.0. Use this as a decision input, not as a standalone conclusion.
B is -3.0. Use this as a decision input, not as a standalone conclusion.
C is 2.0. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Root 1

Root 2

Equation type

Scenario B

Root 1

Root 2

Equation type

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

Formula References

Algebra and arithmetic identities used by the selected formula.
Standard precision arithmetic; rounding shown for readability.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

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