Equation Solver
Finds the real solutions of an equation in x, including ones no formula can give you.
Results
What this tool does
Write the equation the way you would on paper — with an equals sign, or just the expression if it is already set to zero — and it is solved numerically: everything moves to one side, the range is swept looking for the moment the value crosses zero, and each crossing is narrowed down by repeated halving until it is exact to eight decimal places. That method does not care whether the equation is a polynomial: sin(x) = 0.5 and exp(x) = 5 are no harder than 2x + 3 = 11, and neither has a formula you could apply by hand.
Formula
moves everything to one side and looks for where the function changes sign, narrowing down by bisection
Variables
| Symbol | Meaning | Unit |
|---|---|---|
equation | Equation in x | — |
x_min | Search from x = | — |
x_max | Search up to x = | — |
OUT | Solutions | — |
NR | Solutions found | — |
R1 | First solution | — |
R2 | Second solution | — |
Worked example
- Equation in xx^2 - 5*x + 6 = 0
- Search from x =-100
- Search up to x =100
- Solutions2 3
- Solutions found2
- First solution2.00000000
- Second solution3.00000000
Limitations
- The calculation runs entirely in your browser. The values you type are never sent to a server.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
Why does it miss some solutions?
Because it finds solutions by watching for the curve to cross zero, and a curve that only touches zero without crossing leaves no sign change to find. The root of x² = 0 is exactly that case: the parabola grazes the axis at x = 0 and comes straight back up. It also only looks inside the range you give it, so widening the range finds solutions that lie further out, and narrowing it separates two roots that are very close together. For a quadratic with real coefficients, the dedicated quadratic page uses the exact formula instead.