Solving linear equations
A linear equation like ax + b = c is solved by isolating x: subtract b from both sides, then divide by a, giving x = (c - b) / a. This calculator shows each of those steps explicitly rather than just the final answer, which is useful for checking homework or refreshing the process before an exam. Linear equations always have exactly one solution (unless a = 0, in which case there's either no solution or infinitely many, depending on b and c).
Solving quadratic equations
A quadratic equation, ax² + bx + c = 0, is solved using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The expression under the square root (b² - 4ac) is called the discriminant, and it tells you what kind of solutions to expect before you even finish the calculation: positive means two distinct real solutions, zero means exactly one repeated real solution, and negative means the solutions are complex (involve imaginary numbers).
Frequently asked questions
What if the discriminant is negative? The equation has no real solutions -- only complex ones involving i (the imaginary unit). This is common and not an error; it just means the parabola never crosses the x-axis.
Can this solve systems of equations? This calculator handles single-variable linear and quadratic equations. For systems of two or more equations with multiple variables, you'd need a system-solving tool that uses substitution or matrix methods instead.
Why show the steps instead of just the answer? Seeing each algebraic move -- what got subtracted, what got divided -- is what actually builds the skill to solve the next equation without a calculator, which is the point if you're studying rather than just checking a number.