Free collection of advanced algebra calculators for solving equations, polynomials, and inequalities.
Solve quadratic, cubic, linear, simultaneous equations, and polynomial expressions instantly.
Perfect for students, teachers, and engineers - works on any device with no download required.
Must be non-zero for a quadratic equation
Enter coefficients to see the equation
Enter coefficients a, b, and c to solve the quadratic equation.
Select the type of equation or algebraic problem you want to solve from the dropdown menu
Enter your equation or problem details in the input fields provided
Specify any additional parameters (like the number of solutions or precision level)
Click the 'Solve' button to get instant step-by-step solutions
Review the detailed solution with explanations and download or share results if needed
Calculate when a projectile reaches maximum height using quadratic equations
Determine break-even point for a business using linear equations
Solve simultaneous equations for complex electrical circuits
Balance chemical equations using algebraic methods
Find equilibrium price where supply equals demand
Verify algebra homework solutions, understand step-by-step problem solving, and practice different types of equations. Perfect for high school algebra, college mathematics, and self-study.
Generate example problems with solutions, create practice worksheets, and demonstrate different solving methods. Helps teachers explain complex algebraic concepts visually.
Solve real-world engineering problems involving optimization, curve fitting, and system analysis. Essential for mechanical, electrical, and civil engineering calculations.
Calculate break-even points, optimize profits, model supply-demand relationships, and solve compound interest problems. Critical for business planning and investment analysis.
Analyze experimental data, fit curves to data points, solve optimization problems, and model natural phenomena using algebraic equations.
Algebra is the branch of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations. At its core, algebra helps us find unknown values by establishing relationships between variables. Linear equations represent straight-line relationships where variables appear only to the first power, while quadratic equations involve squared terms and can represent parabolas or projectile motion.
Quadratic equations follow the standard form ax² + bx + c = 0 and can be solved using the quadratic formula: x = (-b ± √(b²-4ac))/2a. The discriminant (b²-4ac) determines the nature of roots - positive discriminants yield two real solutions, zero gives one real solution, and negative discriminants result in complex conjugate solutions. These equations model many real-world phenomena from physics to finance.
Cubic equations and higher-degree polynomials become increasingly complex but follow similar principles. The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots (including complex ones). Simultaneous equation systems represent multiple constraints on variables and are solved using substitution, elimination, or matrix methods. These systems are crucial in optimization problems where multiple conditions must be satisfied simultaneously.
Forgetting to check extraneous solutions
Always verify your solutions by plugging them back into the original equation. Some operations (like squaring both sides) can introduce extraneous solutions that don't satisfy the original equation.
Incorrect sign handling in quadratic formula
Pay special attention to negative signs when applying the quadratic formula. Remember that -b ± √(b²-4ac) means both negative b and the square root term need careful sign management.
Not considering all possible solutions
Quadratic equations always have two solutions (they might be equal or complex). Don't stop after finding one solution - check for additional roots that might be real, complex, or repeated.
Improper setup of word problems
Carefully translate word problems into equations. Define variables clearly, identify the relationships given in the problem, and ensure your equation accurately represents the situation described.
Division by zero when simplifying expressions
Never divide by an expression that could equal zero. When canceling factors, first check if those factors could be zero for some values - these might be valid solutions you're excluding.
Our calculators handle linear equations, quadratic equations (including complex roots), cubic equations, polynomial equations up to 10th degree, simultaneous equation systems, and linear/quadratic inequalities.
Our calculators provide solutions with high precision (up to 10 decimal places) and include step-by-step explanations. Complex number solutions are displayed in both rectangular and polar forms when applicable.
Absolutely! These calculators are perfect for verifying homework answers, understanding solution methods, and learning algebra concepts. The step-by-step solutions help you understand the process, not just get the answer.
Yes, all our algebra calculators provide detailed step-by-step solutions including the formulas used, intermediate calculations, and final answers. This helps with learning and understanding the problem-solving process.
Yes, these calculators handle advanced topics including complex numbers, high-degree polynomials, and sophisticated equation systems. They're suitable for college-level algebra, engineering mathematics, and scientific calculations.
While our calculators solve the mathematical equations, you'll need to first translate word problems into algebraic equations. Once you have the equation form, our calculators can find the solutions quickly.
No, your calculations are not saved permanently. All computations happen in your browser, and your equations and results are cleared when you refresh the page, ensuring complete privacy.
The calculators require an internet connection initially to load, but once loaded, they can perform calculations offline. For best performance and features, keep your internet connection active.