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Certified calculator · Version 1

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 degree2
CalcuMint Pro

Advanced Analysis

Compare plans
Advanced chartsExplore the result across time and assumptions.
Scenario comparisonCompare multiple assumptions side by side.
Sensitivity analysisSee which assumptions change the outcome most.
Goal SolverSolve backwards from the outcome you want.
Result methodology

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

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.

  • 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.