Solve linear and quadratic equations and evaluate algebraic expressions step by step.
The Math Equation Solver handles three of the most common algebra tasks students face: solving a linear equation of the form ax + b = c, solving a quadratic equation of the form ax² + bx + c = 0, and evaluating a general numeric expression that may include parentheses, exponents, and the standard order of operations. Rather than working through each step by hand every time, or reaching for a physical calculator that cannot show its working, this tool solves the equation and displays the method used to reach the answer.
For a linear equation, enter the coefficients a, b, and c representing ax + b = c, and the tool isolates x by subtracting b from both sides and dividing by a, showing the resulting value of x along with a note if a is zero (which makes the equation either impossible or true for all x, depending on the other values). For a quadratic equation, enter a, b, and c representing ax² + bx + c = 0, and the tool applies the quadratic formula, x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a. It calculates the discriminant (b² minus 4ac) first and reports whether the equation has two distinct real roots, one repeated real root, or two complex roots, showing the appropriate result for each case rather than only handling the straightforward positive- discriminant scenario.
The "Evaluate an expression" mode accepts a general arithmetic expression using standard notation: multiplication with *, division with /, and exponents with ^, along with parentheses for grouping. This is useful for quickly checking arithmetic in a longer word problem, verifying a calculation from a textbook example, or evaluating a formula after substituting in numeric values by hand, without needing to open a separate calculator app or risk a typo on a physical calculator's small screen.
This tool covers foundational algebra rather than calculus, matrix operations, or systems of multiple equations; for those more advanced tasks, a dedicated computer algebra system or the Scientific Calculator tool on this site (for trigonometric and logarithmic evaluation) will be more appropriate. The goal here is fast, reliable handling of the linear and quadratic equations that appear constantly throughout middle school, high school, and introductory college algebra coursework.
Every calculation is performed locally using JavaScript running in your browser, so equations you enter, including any from an unpublished exam or homework set, are never transmitted anywhere.
Working through the same problem by hand alongside the tool's displayed steps, rather than only reading off the final answer, is generally a more effective way to build the underlying algebra skill being tested, since exam settings will not have this calculator available and the goal of most coursework is fluency with the method itself, not just the final numeric result.
When entering coefficients, remember that a very small or very large number can sometimes produce results in scientific notation that are hard to read at a glance; if that happens, consider simplifying the equation by hand first (for example dividing every coefficient by a common factor) before entering it, which usually produces a cleaner, more readable result.
If a is zero, the equation reduces to b = c. The tool reports whether this is always true (infinite solutions) or never true (no solution) rather than attempting to divide by zero.
It means the equation has no real solutions, only two complex (imaginary) roots, which the tool will display in the standard a ± bi form.
No, this tool solves a single linear or quadratic equation at a time. Systems of multiple equations would need a different, more advanced tool.
Standard arithmetic operators: + - * / for addition, subtraction, multiplication and division, ^ for exponents, and parentheses for grouping.
No, this tool covers linear and quadratic algebra and basic expression evaluation only. For trigonometric, logarithmic, or more advanced evaluation, use the Scientific Calculator tool.
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