How do I solve an equation on the calculator?

Switch to EQN mode, choose the equation type (polynomial degree 2 or 3, or simultaneous in 2–3 unknowns), enter the coefficients, and press = to read the roots or solution.

Does the solver return complex roots?

Yes. When a quadratic or cubic has no real solution, the solver returns the complex roots in a+bi form, so x²+1=0 gives ±i.

How many unknowns can the simultaneous solver handle?

Linear simultaneous equations in 2 or 3 unknowns, matching the Casio fx-991ES PLUS. Enter each equation's coefficients and the constant term.

Online Equation Solver: Quadratic, Cubic & Simultaneous

Q: What does the discriminant tell me?

For a quadratic ax²+bx+c, the discriminant b²−4ac shows the nature of the roots: positive means two distinct real roots, zero means one repeated real root, and negative means a complex-conjugate pair.

An online equation solver does the algebra you'd otherwise grind through by hand — and returns complex roots without complaint. Our solver lives in EQN mode and covers quadratics, cubics and simultaneous linear equations. Here's how each works.

Using EQN mode

Switch to EQN mode and pick the type: a polynomial of degree 2 (quadratic) or 3 (cubic), or a simultaneous system in 2 or 3 unknowns. Then enter the coefficients in order and press =. Use the arrow keys to step through multiple roots.

Quadratic equations

For ax² + bx + c = 0, enter a, b, c.

Two real roots

x² − 5x + 6 = 0 → enter 1, −5, 6 → x = 2 and x = 3.

Complex roots

x² + 1 = 0 → enter 1, 0, 1 → x = i and x = −i.

Every solution method behind these answers is in solving quadratics (every method).

Cubic equations

For ax³ + bx² + cx + d = 0, enter a, b, c, d.

Three real roots

x³ − 6x² + 11x − 6 = 0 → enter 1, −6, 11, −6 → x = 1, 2, 3.

One real, two complex

x³ − 1 = 0 → enter 1, 0, 0, −1 → x = 1 and a complex-conjugate pair.

Simultaneous equations

Choose 2 or 3 unknowns and enter each equation's coefficients and constant.

Two unknowns

2x + y = 5 and x − y = 1 → enter (2, 1, 5) and (1, −1, 1) → x = 2, y = 1.

The full workflow, including three unknowns, is in systems of equations with 2–3 unknowns — and the matrix view is in solving simultaneous equations with matrices.

Reading the roots

For a quadratic, the discriminant b² − 4ac tells you what to expect before you even solve:

Discriminant	Roots
b² − 4ac > 0	Two distinct real roots
b² − 4ac = 0	One repeated real root
b² − 4ac < 0	Complex-conjugate pair

When roots come out complex, the complex number calculator guide shows how to interpret them.

Frequently asked questions

How do I solve an equation?

In EQN mode, pick the type, enter coefficients, and press = for the roots or solution.

Does it return complex roots?

Yes — when there's no real solution, roots are returned in a+bi form.

How many unknowns for simultaneous?

2 or 3, entered as coefficient rows with constants.

What does the discriminant tell me?

b²−4ac: positive → two real, zero → one repeated, negative → complex pair.

Solve it now

Open EQN mode, choose your equation type, and enter the coefficients.

Open the online equation solver →