Equation Solver: Solve Linear & Quadratic Equations | Free

A When Δ < 0, the equation has two complex conjugate roots. The solver shows both the real and imaginary parts.

A Currently, this tool supports linear and quadratic equations. Cubic and higher-degree equations are planned for a future update.

A The solver shows each calculation step: substituting values, computing the discriminant, and applying the formula.

A This free equation solver is an excellent study aid for algebra exams. It allows you to quickly verify your solutions for linear and quadratic equations. By comparing your manual steps with the tool's detailed step-by-step solutions, you can identify errors, understand correct methodologies, and build confidence for your upcoming test. It's perfect for reviewing concepts like the discriminant and complex roots.

A Yes, this free online equation solver is fully optimized for mobile devices. You can access it directly through your web browser on any smartphone or tablet – no app download required. Its responsive design ensures a seamless experience for solving linear and quadratic equations with detailed step-by-step solutions, making it perfect for studying anywhere, anytime.

A You can input linear equations in the form ax + b = 0, where 'a' and 'b' are numbers. For quadratic equations, use the format ax² + bx + c = 0. Ensure you use standard mathematical notation, for instance, '2x+5=0' or '3x^2-7x+2=0'.

A That happens when the discriminant (b²-4ac) is negative. For example, x²+2x+5=0 gives Δ = 4-20 = -16. No real number squared equals a negative, so the parabola never crosses the x-axis. The tool still shows the complex roots like -1±2i. Try changing the 'c' value to something smaller, like 2, to get real solutions.

A Yes, it does. When the discriminant is negative, the solver displays complex roots in a+bi form. For instance, x²+4x+13=0 gives you -2±3i. It also highlights that the real part comes from -b/2a and the imaginary part from √(|Δ|)/2a. Chemistry teachers use this to show students how math maps onto wave functions. Try plugging in values with small 'a' coefficients to see cleaner imaginary parts.

A You'll need to rearrange them first. The tool expects ax+b=0 for linear or ax²+bx+c=0 for quadratics. For something like 5 = 3x-2, rewrite it as 3x-7=0. Same for quadratics—if you have x² = 6x-8, put it as x²-6x+8=0. Then paste it in. The solver only works with the left side set to zero, so take that extra step. A quick tip: check your signs when moving terms across the equals sign.

A Just type them straight in. Use 0.5 for 1/2, or 3.14159 if you're feeling precise. The solver handles decimal coefficients without any issues. For something like ⅔x² + 0.75x - 1.2 = 0, input it as 0.6667x^2+0.75x-1.2=0. The step-by-step solution will show the discriminant and roots in decimals. One catch: avoid using the slash symbol for fractions—the parser expects decimal points.