Equation Solver

What the solver handles

Worked example

x^2 - 5x + 6 = 0

Step 1: Identify a=1, b=-5, c=6. Step 2: Compute the discriminant: D = 25 - 24 = 1. Step 3: D > 0 means two real roots. Step 4: Apply the quadratic formula: x = (5 +/- 1) / 2. Step 5: Roots: x = 3 and x = 2. Step 6: Verify: 9 - 15 + 6 = 0 ✓ and 4 - 10 + 6 = 0 ✓.

Linear equations

A linear equation ax + b = 0 has one root: x = -b/a. If a = 0 and b = 0, every value of x satisfies the equation; if a = 0 and b is not zero, there is no solution. The solver reports both cases.

Complex roots

When the discriminant is negative, the quadratic has no real roots. The solver shows the complex conjugate pair as real + imagi and real - imagi. For example, x^2 + 4 = 0 gives the roots 0 + 2i and 0 - 2i.

What the solver does not do

This solver handles one linear or quadratic equation with numeric coefficients. It does not parse typed-in equations, solve cubic or higher-degree polynomials, handle equations with absolute values or roots, or solve systems of equations. Use a dedicated tool for those cases.

Common mistakes

• Sign errors. The most common cause of unexpected roots. Check every coefficient, especially b in x^2 - 5x + 6 = 0: -5 is not the same as 5.
• Expecting real roots when the discriminant is negative. A negative D means the roots are complex, not that you entered the wrong numbers. Verify D = b^2 - 4ac when in doubt.
• Forgetting the a = 0 case. With a = 0 the equation becomes linear; the solver handles it automatically.