Quick start
- Write the equation with a single = sign, for example 3^x = 20 or x^3 = 2x + 1. Use ^ for powers, sqrt() for square roots, and ln() or log() for logarithms.
- The solver looks for answers between −100 and 100. Widen or narrow that window if you expect something else.
- Each answer comes with a check line showing the value of the left side and the right side.
What happens behind the scenes
The tool rewrites your equation as f(x) = left side − right side, which equals 0 at every solution. It samples f across the range, spots every place where the sign flips from positive to negative or back, and then keeps halving that small interval until the answer is pinned down to about ten significant figures. This method is called bisection.
Example: 3^x = 20
By hand you would take logs of both sides: x · ln 3 = ln 20, so x = ln 20 ÷ ln 3 ≈ 2.7268. The solver reaches the same number without any algebra, and the check confirms that 3 raised to that power is 20.
Writing equations it understands
- Multiplication can be written 4x, 4*x or 4(x − 1).
- Trig functions work in radians. For degrees, write sin(x*pi/180).
- Use e^x or exp(x) for the exponential function.
Common questions
It says no real solution. What now?
Some equations have none, such as x² + 4 = 0. Otherwise the answer may sit outside the search window, so try a wider range.
Can it solve x = cos(x)?
Yes. There is no exact formula, but the solver finds x ≈ 0.7391 numerically.
Does it give complex answers?
No. It only finds real values of x. For complex roots of a quadratic, use the Quadratic Equation Solver.
How many solutions can it show?
Up to 25 in one search. If an equation like sin(x) = 0.5 has more, narrow the range to see the rest.