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Solve for x Calculator with steps

Type one equation, choose the letter to solve for and get exact solutions, each one checked by substituting it back into your equation.

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Answer

Enter your numbers or pick an example — the answer and the steps appear here instantly.

How to solve an equation here

  1. Type the equation

    Write it the way you would on paper. 3(x − 2) + 5 = 2x + 7 works as typed, with implicit multiplication, ², √ and π accepted.

  2. Name the variable

    Any single letter works, so a literal equation such as 2x + 3y = 7 can be solved for x or for y.

  3. Press Calculate

    The solver moves every term to one side, collects like terms and picks a method that suits the equation it finds.

  4. Read the checked answers

    Each solution is substituted back into the original equation before it is listed. Approximate roots carry the ≈ sign.

Which method it uses

The outline names the approach, so you can practice the same one on paper.

  • Linear equations

    Terms are collected and the variable is isolated, so 3(x − 2) + 5 = 2x + 7 becomes 3x − 1 = 2x + 7 and then x = 8.

  • Quadratic equations

    The outline lists a, b and c, computes the discriminant b² − 4ac and applies the quadratic formula with the radical simplified: x² − 2x − 1 = 0 gives x = 1 ± √2.

  • Polynomials up to degree 10

    The rational root test proposes candidates and synthetic division removes each root it confirms. What remains goes to the quadratic formula or, with no rational roots left, to a numerical method.

  • Complex roots

    A negative discriminant produces a complex pair instead of a bare “no solution”: x² + 2x + 5 = 0 gives x = −1 ± 2i.

  • Exponential and trig equations

    For equations like 2^x = 8 or sin x = 1/2, a verified exact root is shown when one is found; otherwise you get numeric roots between −20 and 20, marked ≈.

  • Identities and contradictions

    If both sides always agree, as in 2(x + 1) = 2x + 2, every value is a solution. If they never can, as in x + 1 = x + 3, you are told there is none.

How to solve for x by hand

The rule behind every step is balance: whatever you do to one side of an equation, do to the other. Adding or subtracting the same quantity, or multiplying or dividing both sides by the same nonzero number, keeps the solutions unchanged. Take 5x − 4 = 2x + 11. Subtract 2x from both sides to get 3x − 4 = 11, add 4 to get 3x = 15, then divide by 3 to reach x = 5.

Quadratics need a different idea, because the variable appears squared. Bring everything to one side so the equation reads ax² + bx + c = 0, then factor or use x = (−b ± √(b² − 4ac)) / 2a. For 2x² + x − 6 = 0 you have a = 2, b = 1 and c = −6, so the discriminant is 1 + 48 = 49 and x = (−1 ± 7) / 4, giving x = 3/2 or x = −2.

Finish with a check. Substitute each answer into the original equation rather than a rearranged line, since an early slip carries through every later step. Dividing by an expression that contains x, or squaring both sides, can lose or invent solutions, so those are the moments when the check matters most.

Frequently asked questions

Yes. Type any single letter in the variable box. A literal equation such as 2x + 3y = 7 solved for x gives x = (7 − 3y)/2, with the other letters treated as constants.

It handles polynomial equations up to degree 10. Rational roots come out exact, a leftover quadratic factor goes through the quadratic formula, and anything beyond that is approximated numerically and marked ≈.

A negative discriminant means the quadratic has no real roots. The calculator then gives the complex pair, like −1 ± 2i; if your class only wants real solutions, the answer is that none exist.

They do not. Natural log is written ln (base e) and log is base 10, so the solution of log(x) = 2 is x = 100.

The solver, its step outline and the substitution checks are free and run in your browser without an account. A full written explanation from the AI Math Solver is included in the Pro plans* (*fair use: up to 300 runs a day across the writing, study and code tools) or uses 2 credits without a plan; while signed out you can read its start as a free preview.

Use it to check answers you have already worked out and to see which method fits. Follow your teacher's rules on AI tools, and remember that the AI explanation, unlike the substitution-checked solutions, can contain mistakes.

Keep practicing algebra

Have an equation to solve?

Type it in, pick the variable and get exact solutions that have been substituted back.

Solve for x
  • Exact radicals and fractions
  • Every root checked
  • Polynomials up to degree 10