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Equation Solver

Solve linear and quadratic equations step by step.

Linear or quadratic, with one letter. Use ^ or ² for squares, and brackets as needed.

Try:

Answer

x = 4

Step by step

  1. 1

    Start with the equation

    2x + 3 = 11

  2. 2

    Get x terms on one side and numbers on the other

    2x = 8

    Subtract 3 from both sides.

  3. 3

    Divide both sides by 2

    x = 8 ÷ 2 = 4

  4. 4

    Check the answer

    Left side = 11, right side = 11 ✓

    Put x = 4 back into the original equation. Both sides match.

When to use it

Use this tool to solve linear and quadratic equations and see every step of the working. It is made for students checking homework, parents helping with algebra, and anyone who wants to understand how an answer was reached rather than just seeing the number.

How to use it

  1. Type your equation into Equation, such as 2x + 3 = 11. On a phone, use the symbol buttons for x, ², brackets and operators.
  2. Click Solve, or tap one of the examples next to Try.
  3. Read the Answer at the top.
  4. Follow Step by step to see how it was solved. Each step has a short title, the maths and a note explaining why.

Worked example: a linear equation

Solve 2x + 3 = 11. The steps are:

  1. Start with the equation: 2x + 3 = 11.
  2. Subtract 3 from both sides to get x terms on one side: 2x = 8.
  3. Divide both sides by 2: x = 8 ÷ 2 = 4.
  4. Check the answer by putting x = 4 back in: both sides equal 11.

Worked example: a quadratic

Solve x² − 5x + 6 = 0. The tool identifies a = 1, b = −5 and c = 6, then works out the discriminant: D = (−5)² − 4 × 1 × 6 = 1. Because D is positive, there are two answers. Using the quadratic formula, x = (5 ± 1) ÷ 2, so x = 2 or x = 3.

Sharing a problem

You can open the solver with an equation already filled in by adding ?eq= and the equation to the page address, for example ?eq=3x%2B1%3D10 for 3x + 1 = 10. Teachers can use this to prepare links for a class worksheet, so each link opens on a different question.

Tips

  • Check by substituting. Put your answer back into the original equation. If both sides match, it is right.
  • Use brackets carefully. 3(x − 2) means 3 times everything in the brackets.
  • Read the notes. They explain the reason for each step, which is what teachers look for.
  • Try the examples. They show the range of equations the tool can handle.
  • Simplify fractions first if you like. Multiplying every term by the same number can make an equation with fractions easier to follow.

Common mistakes

  • Doing something to only one side. Whatever you do to one side, you must do to the other.
  • Losing a minus sign. Subtracting a negative number is the same as adding.
  • Forgetting the second answer. Most quadratics have two solutions.
  • Typing two different letters. The tool solves for one unknown at a time.

Frequently asked questions

What kinds of equations can it solve?

Linear equations like 3(x − 2) = 2x + 4 and quadratic equations like x² − 5x + 6 = 0, with one letter. It handles brackets, fractions such as x/4, and powers up to squared.

What if a quadratic has no real solutions?

When the discriminant (b² − 4ac) is negative, there are no real-number answers. The tool explains this and shows the complex solutions, which use i, the square root of −1.

Can I use a letter other than x?

Yes. Any single letter works, such as y = 2y − 5 or 3t + 1 = 10. The equation must use only one letter.

How do I type a square?

Type ^2, use the ² button, or write x*x. Use the buttons above the box on a phone for symbols like ×, ÷ and brackets.

Should I just copy the answer for homework?

Use the steps to understand the method, then try a similar question yourself. Teachers usually want to see working, and practising is what helps in tests.

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