Solve linear and quadratic equations with detailed step-by-step solutions
Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations. This calculator helps you solve linear and quadratic equations, which are fundamental concepts in algebra used across mathematics, science, engineering, and everyday problem-solving.
Linear equations have one variable raised to the first power and produce a straight line when graphed.
Isolate the variable by performing inverse operations on both sides of the equation.
2x + 3 = 7 → x = 2
Quadratic equations have a variable raised to the second power and produce a parabola when graphed.
Use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
x² - 5x + 6 = 0 → x = 2 or x = 3
For quadratic equations, the discriminant (Δ = b² - 4ac) determines the nature of the solutions:
Two distinct real solutions
One repeated real solution
Two complex solutions
Calculating projectile motion, velocity, acceleration, and force relationships
Designing structures, circuits, and systems with optimal parameters
Computing interest rates, investment returns, and break-even points
Analyzing supply and demand curves, cost functions, and market equilibrium
Algorithm analysis, optimization problems, and computational complexity
Budgeting, recipe scaling, distance-time calculations, and planning
Symbols (usually letters) that represent unknown values or quantities that can change
Numbers that multiply variables (e.g., in 3x, the coefficient is 3)
Fixed numerical values that don't change in an equation
Mathematical actions like addition, subtraction, multiplication, and division
Calculate percentages and percentage changes
Calculate percentage increase
Calculate percentage decrease
Calculate percentage difference
Calculate with fractions
Calculate ratios and proportions