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Formula verified · Deterministic calculation

Equation Solver

Enter coefficients for ax²+bx+c=0. The certified engine automatically uses the linear solver when a=0 and the stable quadratic solver otherwise.

Solution(s)3, 2
Equation degree
2
Methodology

The certified equation engine dispatches validated coefficients to deterministic linear or stable quadratic solving.

Sources
  • CalcuMint deterministic equation engine
Solution steps
  1. D = 1
  2. Solutions: 3, 2

How this calculator works

Linear equations use x=-c/b. Quadratics use the discriminant and a numerically stable quadratic formulation, including complex conjugate solutions.

Formula

ax²+bx+c=0

Deterministically dispatches first- and second-degree equations to stable algebraic solvers.

Worked example

x²-5x+6=0 is a verified test case used by the calculation engine.

Assumptions and limitations

  • At least one x coefficient must be non-zero.
  • Inputs are finite real numbers.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.

  • CalcuMint deterministic equation engine — Linear isolation and numerically stable quadratic formula.

Frequently asked questions

Which equations are supported?

First- and second-degree equations in one variable.

Are complex roots supported?

Yes. Quadratics with a negative discriminant return complex conjugate solutions.

Related calculators

Linear Equation SolverSolve ax + b = 0 with deterministic algebra steps.Quadratic Formula CalculatorSolve quadratic equations and inspect discriminant, roots and vertex.Polynomial CalculatorFind the distinct real roots of a cubic polynomial.
Equation Solver | CalcuMint