Equation Solver

This equation solver handles almost any equation in one variable, including polynomial, exponential and trigonometric equations that have no simple formula. It moves everything to one side, searches the chosen range for sign changes, narrows each one down by bisection, and graphs both sides so you can see where they meet. Linear equations are solved exactly.

Try:

How to use the equation solver

  1. Type the equation with one = sign, using x.
  2. Optionally change the range of x to search.
  3. Press Calculate to see the solutions and the graph.

Formula

f(x)=g(x)  ⟺  f(x)−g(x)=0f(x) = g(x) \iff f(x) - g(x) = 0

Worked example: x³ − 2x = 4

  • Equation: x^3 - 2x = 4
  • Search x from: -20
  • to: 20

◐ Partly checked

x≈2x \approx 2
Number of solutions found
1
−11234520406080100x ≈ 2left sideright side
The solutions are the x-values where the two graphs cross.
Step-by-step working (2 steps)

  1. Move everything to one side

    Solve f(x) = 0 where f is the left side minus the right side.

    x3−2x−4=0x^{3} - 2x - 4 = 0

  2. Find where the graphs meet Bisection method

    Scan the range for sign changes of f(x), then narrow each one down by repeated halving (bisection).

    x≈2x \approx 2
How this was checked
  • ✓ Substituting each solution makes both sides equal (to rounding).

Solutions are searched for between -20 and 20; a solution where the graphs only touch without crossing may be missed.

Frequently asked questions

Can it solve equations without a formula, like 2^x = x + 3?

Yes. It finds the solutions numerically, accurate to about 10 significant figures, and labels them as partly checked.

Why might it miss a solution?

It looks for places where the two sides cross. If the graphs only touch, or the solution is outside the range, widen the range or use a dedicated solver.

Does it show exact answers?

For linear equations, yes. For quadratics, the quadratic equation solver gives exact surd answers.

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