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Equation Solver

Solve linear and quadratic equations and see step-by-step working.

Equation form: ax + b = c

Solution

2x − 3 = 7
2x = 7 + 3
2x = 10
x = 10 ÷ 2
x = 5

About this tool

Equation Solver finds the solution to linear equations (ax + b = c) and quadratic equations (ax² + bx + c = 0), showing every algebraic step along the way. For linear equations it walks through the rearrangement until x is isolated. For quadratics it computes the discriminant, tells you whether the roots are real or complex, and applies the quadratic formula with your actual numbers. The step-by-step output makes it easy to check homework answers, understand a method, or verify a solution quickly.

How to use

  1. Choose Linear or Quadratic mode.
  2. Enter the coefficients a, b, and c.
  3. The solution and working appear on the right.

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FAQ

What is the difference between linear and quadratic modes?

Linear solves ax + b = c, which always has exactly one solution. Quadratic solves ax² + bx + c = 0, which can have two real roots, one repeated root, or two complex roots depending on the discriminant.

What does the discriminant tell you?

The discriminant is b² − 4ac. If it is positive, there are two distinct real roots. If it is zero, there is exactly one real root (repeated). If it is negative, the roots are complex — they contain the imaginary unit i.

Can it solve equations with fractions or decimals as coefficients?

Yes. The coefficient inputs accept any decimal number.

What does 'a cannot be 0' mean?

For a linear equation, a is the coefficient of x — if it is 0 there is no x term and the equation is not linear. For quadratic, a = 0 means there is no x² term, making it a linear equation — switch to Linear mode.

Does it show the working?

Yes. For linear equations it shows each algebraic step. For quadratic it shows the discriminant calculation and then the root formula applied with the actual numbers.