How is the discriminant computed?

Δ = b²-4ac. Δ>0 gives two distinct real roots, Δ=0 a repeated root, and Δ<0 a pair of complex conjugate roots, which are shown as well.

The quadratic degenerates into the linear equation bx+c=0; the tool says so and solves that instead.

How do I know a system has no unique solution?

Check the determinant D = a₁b₂ - a₂b₁. When D = 0 the equations are proportional, so there is either no solution or infinitely many.

Can I use decimal coefficients?

Yes — decimals and negatives are supported, and results are given to 10 significant digits.

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🟰Online Equation Solver - Linear, Quadratic, Cubic and 2×2 Systems

Q: What if a is 0?

The quadratic degenerates into the linear equation bx+c=0; the tool says so and solves that instead.

Q: How do I know a system has no unique solution?

Check the determinant D = a₁b₂ - a₂b₁. When D = 0 the equations are proportional, so there is either no solution or infinitely many.

Q: Can I use decimal coefficients?

Yes — decimals and negatives are supported, and results are given to 10 significant digits.

Enter the coefficients and get the solution. Quadratics also show the discriminant, real or complex roots, the vertex, the axis of symmetry, the factored form and the sum and product of the roots; systems show the determinant and Cramer’s rule.

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How to use Equation Solver

1Pick the equation type: linear, quadratic, cubic or a 2×2 system
2Fill in each coefficient (decimals and negatives are fine)
3Read the answer and the working, and copy what you need

FAQ

How is the discriminant computed?: Δ = b²-4ac. Δ>0 gives two distinct real roots, Δ=0 a repeated root, and Δ<0 a pair of complex conjugate roots, which are shown as well.
What if a is 0?: The quadratic degenerates into the linear equation bx+c=0; the tool says so and solves that instead.
How do I know a system has no unique solution?: Check the determinant D = a₁b₂ - a₂b₁. When D = 0 the equations are proportional, so there is either no solution or infinitely many.
Can I use decimal coefficients?: Yes — decimals and negatives are supported, and results are given to 10 significant digits.