Equation Solver: Solve Linear & Quadratic Equations | Free

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.

A It won't work unless you clean it up first. The parser expects exactly 'ax+b=0' or 'ax²+bx+c=0'. That equation needs rewriting to 'x+10=0'. For something like 'x²-5 = 4x-1', rearrange all terms to one side: 'x²-4x-4=0'. Three specific checks: move everything left of equals, combine like terms, and double-check your signs. A sign error flips the whole solution.

A That's a double root. It happens when the discriminant equals zero, like in x²-6x+9=0 where Δ=0. The parabola touches the x-axis at exactly one point, x=3. Your textbook calls this a repeated root. The solver shows 'x=3, x=3' anyway because the quadratic formula still produces two values, just identical ones. Physics teachers use this for projectile problems where an object just barely grazes the ground.

A No, not directly—you have to rearrange first. The parser only reads 'ax+b=0' or 'ax²+bx+c=0'. For '4x-3=2x+5', subtract 2x and add 3 to get '2x-8=0'. That's a 30-second fix, but it's the #1 cause of wrong entries. The tool won't auto-move terms, so don't skip that step. A quick check: plug your final answer back into the original equation. If both sides match, you're good.

A No limit at all. You can solve hundreds of equations in a single session without signing up or paying anything. Each run takes under a second, even on a basic phone connection. For homework sets with 20 quadratics, just paste them one at a time and copy the steps. The tool recalculates instantly, so batch work moves fast. One tip: refresh the page every 30 or so problems to avoid browser memory bloat if you're on an older device.

A Copy it, yes. Paste it as your own work, no. Teachers spot identical step formatting fast, and the real value here is checking your process. Work the problem by hand first, then compare. For 2x²-8x+6=0, you should get x=1 and x=3. If your scratch work says something else, the steps show exactly where things went sideways. Use it like an answer key, not a substitute.

A Build your own tests backward by picking whole number roots first. For instance, if you want answers at x=2 and x=-5, multiply (x-2)(x+5) to get x²+3x-10=0. Plug that polynomial into our solver to generate the full step-by-step breakdown instantly. Tutors use this trick to avoid messy decimals that confuse students. Test your custom equation here before printing your quiz.

A The solver handles numbers up to 1e15 before floating-point limits kick in. If you enter something like 1000000000x^2+5x-2=0, the tool still calculates the roots without crashing. But anything past fifteen digits might round off the least significant figures. College students cramming for physics finals usually stick to standard scientific notation instead of typing out twenty zeros. Watch your digit counts on massive word problems.