Algebra homework
Check linear and quadratic results while still seeing the reduced polynomial form used for the solution.
Equation Solver
Solve linear and quadratic equations in x, inspect the reduced polynomial, and see real or complex roots instantly.
Solve an equation in x
Examples: `2x + 5 = 17`, `x^2 - 5x + 6 = 0`, `(x - 3)^2 = 16`.
Reduced form
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Equation type
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a
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b
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c
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discriminant
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Solutions
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How to use this tool
A quick workflow so you can get the result you need without guesswork.
- 1
Enter an equation in one variable such as 2x + 5 = 17 or x^2 - 5x + 6 = 0.
- 2
Click Solve Equation to reduce both sides into standard polynomial form.
- 3
Review the coefficients, discriminant, and computed roots shown underneath the input.
Useful examples
Practical cases where this utility saves time and reduces mistakes.
Engineering formulas
Rearrange small formulas into a solvable polynomial and confirm whether the roots are real or complex.
Interview practice
Use the solver to validate hand-worked answers while learning how coefficients and discriminants behave.
Frequently asked questions
Short answers to the most common questions about the calculator above.
What equations can this solver handle?
It solves one-variable linear and quadratic equations written with x, standard arithmetic operators, and an equals sign, such as x^2 - 4x + 4 = 0.
Can it show complex roots?
Yes. If the discriminant is negative, the solver returns the two complex roots in a + bi form.
Does the equation solver show the standard form?
Yes. It reduces the input into ax^2 + bx + c = 0 so you can inspect the exact coefficients used in the calculation.
Can I use implicit multiplication like 2x?
Yes. Terms like 2x, -3x, and x^2 are supported, provided the equation only uses one variable named x.
Solve Linear and Quadratic Equations Online
This equation solver is designed for common one-variable algebra problems. It accepts a left side and right side separated by an equals sign, reduces the full expression into standard form, and then solves for x. That makes it useful both as a calculator and as a teaching aid when you want to see the coefficients behind the final answer.
Linear equations return a single solution unless the equation is inconsistent or has infinitely many solutions. Quadratic equations return the discriminant and either two real roots, one repeated root, or a complex conjugate pair. All of that is computed locally in your browser.
Helpful for Study, Review, and Quick Validation
Students can check homework, tutors can generate examples during a lesson, and engineers can sanity-check simplified formulas without moving into a symbolic algebra system. A focused browser-based solver is often faster for these cases than a full CAS environment.
Because the page shows the reduced polynomial form, it is also useful for catching mistakes in sign handling and term collection. That extra transparency is often what turns a quick answer into a useful learning step.
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