🧮 Equation Solver
Solving equations is the single most common job students hand to a CAS calculator. This solver takes your equation in x and answers it two ways: exactly for linear and quadratic equations (the quadratic formula, complex roots included), and numerically for everything else — cubics, trig and exponential equations — by hunting roots down in the range you set.
Type the whole equation with its = sign, such as 2*x^2 − 5*x + 2 = 0, or just an expression to set equal to zero.
How to use this calculator
Write the full equation with one = sign, or an expression to set to zero. The numeric range only matters for non-polynomial equations.
- Type your equation — for example x^2 - 5*x + 6 = 0, sin(x) = 0.5 or exp(x) = x + 2.
- For trig or higher-degree equations, set the search range (default −10 to 10) wide enough to hold the roots you expect.
- Press Calculate and read the solutions: exact for linear and quadratic equations, numerical (marked ≈) otherwise.
- Check any solution by substituting it back into your equation — both sides must match.
Equation Solver Worked Example
Solve 2x² − 5x + 2 = 0. This is quadratic with a = 2, b = −5, c = 2. The discriminant is b² − 4ac = 25 − 16 = 9, whose square root is 3. So x = (5 ± 3) / 4, giving x = 2 or x = 0.5. Substitute back: 2(2²) − 5(2) + 2 = 8 − 10 + 2 = 0 ✓, and 2(0.5²) − 5(0.5) + 2 = 0.5 − 2.5 + 2 = 0 ✓.
Frequently asked questions
Which equations are solved exactly?
Linear equations (ax + b = 0) and quadratic equations (ax² + bx + c = 0) are solved exactly with the quadratic formula — including complex roots when the discriminant is negative, shown in a + bi form. The solver first simplifies your equation into standard polynomial form, so x² = 9 or 2(x+3) = x + 10 work exactly too.
How are other equations solved?
Numerically: the calculator scans your chosen range (default −10 to 10) for sign changes and then bisects down to each root to about 8 decimal places. That handles trig, exponential and cubic equations — sin(x) = 0 in the default range returns all seven roots from −3π to 3π.
Can it miss a root?
A root where the curve just touches the axis without crossing (like (x−2)² = 0 for a higher-degree equation) has no sign change and can be missed by the numeric scan — quadratics are immune because they are solved exactly. Roots outside your search range are also not shown; widen the range if you expect more.
How do I enter an equation?
Type both sides with one = sign, in terms of x: for example 2*x^2 - 5*x + 2 = 0, or x^2 = 9. Leaving off the right side assumes = 0. Multiplication can be implied (2x works) and angles are in radians.