Algebra calculator guide
Algebra uses variables to represent unknown values and equations to describe relationships. This calculator handles quadratic equations and two-variable linear systems.
Enter coefficients exactly as they appear in your equation. Results are rounded only for display.
How to use the algebra calculator
- Choose a mode: Select quadratic solver or two-variable system.
- Enter coefficients: Enter the numeric coefficients and constants from your equations.
- Calculate: Review roots or the x and y solution.
Formula and variables
The discriminant determines whether a quadratic has two real roots, one repeated root, or complex roots.
ax² + bx + c = 0; D = b² − 4ac- a — Quadratic coefficient
- Coefficient of x²
- b — Linear coefficient
- Coefficient of x
- c — Constant
- Term without x
Quadratic example
Solve x² − 3x − 4 = 0.
- a
- 1
- b
- −3
- c
- −4
- D = (−3)² − 4(1)(−4) = 25
- x = (3 ± 5) / 2
Result: x = 4 or x = −1
Both values make the original equation equal zero.
Understanding your results
Roots
A root is a value of x that makes the equation true. Complex roots include the imaginary unit i.
Assumptions
- Coefficients are real numbers.
- The system solver assumes two equations have a unique solution.
Limitations
- Expression mode is retained as an input mode but does not perform symbolic simplification.
- Rounded display values may hide small differences.
Common mistakes
- Dropping a negative sign.
- Entering the constant as a coefficient of x.
- Using a = 0 when intending a quadratic equation.
Practical use cases
Homework checking
Verify roots after solving by hand.
Modeling
Solve simple two-variable relationships.
Frequently asked questions
What does the discriminant tell me?
A positive discriminant gives two real roots, zero gives one repeated root, and a negative discriminant gives a complex-conjugate pair.
How do I solve two simultaneous equations?
Enter each coefficient in the two-variable system mode; the calculator applies Cramer’s rule.
Sources and review
- Algebra: Quadratic Equations — NIST Digital Library of Mathematical Functions. Accessed 2026-07-14.
Reviewed 2026-07-14.