Solve equations step by step

This algebra solver handles the two equation types students meet most: linear equations of the form ax + b = c, and quadratic equations of the form ax² + bx + c = 0. Enter the coefficients and it returns the solution along with the working, so you can check your homework and understand the method, not just the answer.

How quadratic equations are solved

The solver uses the quadratic formula, x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the square root, b² − 4ac, is the discriminant. If it is positive there are two real solutions; if it is zero there is one repeated solution; and if it is negative the solutions are a pair of complex conjugates, which the solver displays in the form p ± qi.

More maths tools

Pair this with our graph plotter to visualise where an equation crosses the x-axis, the scientific calculator for general sums, and the equation simplifier.

How to solve algebra step by step

Solving algebra comes down to keeping the equation balanced: whatever you do to one side, you do to the other. Work in this order and most problems fall apart quickly. First, clear any brackets by expanding them. Second, clear fractions by multiplying every term by the common denominator. Third, collect like terms so all the unknowns sit on one side and all the numbers on the other. Fourth, divide by the coefficient of the unknown to leave it on its own. Finally, substitute your answer back into the original equation to check it.

Worked example: solve 3(x + 4) = 5x − 2. Expand the bracket to get 3x + 12 = 5x − 2. Subtract 3x from both sides: 12 = 2x − 2. Add 2: 14 = 2x. Divide by 2: x = 7. Checking, 3(7 + 4) = 33 and 5(7) − 2 = 33, so the algebra solution is correct. Enter the same equation in the solver above and it will show you the result instantly.

Frequently asked questions

What is the discriminant?

It is b² − 4ac, the expression under the square root in the quadratic formula. Its sign tells you how many real solutions an equation has.

Can it solve equations with no real solution?

Yes. When the discriminant is negative, it returns the two complex roots in the form a ± bi.