Equation Solver
Enter any equation in x. We'll scan the interval you choose and find all real roots numerically using bisection + Newton refinement.
How the equation solver works
Solving general nonlinear equations exactly in closed form is impossible for most expressions, so DesmosGraph uses a robust two-stage numerical approach:
- Bracket scan: we evaluate the function at many sample points across your interval, looking for sign changes that indicate a root by the Intermediate Value Theorem.
- Bisection narrowing: for each bracket we halve the interval until it's tight (≈ 10⁻¹²).
- Newton refinement: a final Newton-Raphson polish using a finite-difference derivative gives full double precision.
This combination is reliable: bisection guarantees convergence inside a bracket, and Newton brings full precision quickly. Roots within rounding error of each other are merged automatically.
Limitations
- Roots outside your interval will not be found — widen the interval if you suspect more.
- Repeated (multiple) roots where the curve touches but doesn't cross the axis can be missed by sign-change scans. If you suspect tangent roots, also use the graphing calculator to inspect visually.
- Complex roots are not reported — only real ones.