Type an equation with one unknown and get the answer with every step: linear equations, quadratics using the quadratic formula, and harder equations solved numerically.
What it can solve
- Linear equations such as
5(x − 2) = 3x + 4. Calcist simplifies both sides, moves the x terms to one side and the numbers to the other, divides, and then checks the answer by putting it back in.
- Quadratic equations such as
x² − 5x + 6 = 0, solved with the quadratic formula. You see a, b, c, the discriminant and both solutions, or the complex solutions when there are no real ones.
- Other equations such as
3^x = 81 or sqrt(x) + 2 = 7, solved numerically to about 10 digits.
Use any single letter for the unknown: 4t − 3 = 9 works too. For two or three unknowns at once, use the system of equations calculator.
How to solve a linear equation by hand
Whatever you do to one side, do to the other. Take 5(x − 2) = 3x + 4:
- Expand the brackets: 5x − 10 = 3x + 4
- Subtract 3x from both sides: 2x − 10 = 4
- Add 10 to both sides: 2x = 14
- Divide both sides by 2: x = 7
- Check: 5(7 − 2) = 25 and 3 × 7 + 4 = 25 ✓
The quadratic formula
For any equation of the form ax² + bx + c = 0:
x = (−b ± √(b² − 4ac)) ÷ 2a
The part under the square root, b² − 4ac, is the discriminant. If it's positive there are two real solutions, if it's zero there's one, and if it's negative there are none on the real number line (but two complex ones).
How we checked this
Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:
- 5(x − 2) = 3x + 4 gives x = 7 ✓
- x² − 5x + 6 = 0 gives x = 2 or 3 ✓
- x² + 4 = 0 has no real solution ✓
Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.
Questions people ask
How do I solve for x?
Get x by itself. Undo additions and subtractions first, then multiplications and divisions, doing the same thing to both sides each time. Type your equation above to see each step.
Can it solve quadratic equations?
Yes. It recognizes quadratics automatically, finds a, b and c, and uses the quadratic formula. It shows exact fractions where the answer is rational.
What does 'no solution' mean?
The x terms cancel out and leave something false, like 3 = 5. For example x + 1 = x + 2 has no solution.
What does 'every number works' mean?
Both sides are the same expression, like 2(x + 1) = 2x + 2, so any value of x makes it true.
Does it work with fractions and decimals?
Yes. Type x/4 or 0.5x as you'd write them. Answers that are fractions are shown as fractions and decimals.