Online Algebraic Equation Solver
Solve linear, quadratic, polynomial, and systems of equations with detailed steps. Finds both real and complex roots with discriminant analysis.
Quadratic Equation (ax² + bx + c = 0)
How to use
- Type or paste mathematical equation (e.g. 2x + 5 = 15 or x² - 5x + 6 = 0).
- Specify unknown variable (default x).
- Click calculate.
- View computed real/complex roots and step-by-step algebraic deduction.
Equation Solution Examples
Linear equation: 2x - 8 = 0 → x = 4.
Quadratic equation: x² - 5x + 6 = 0 → D = 25 - 24 = 1, roots x1 = 2, x2 = 3.
No real roots: x² + 4 = 0 → complex conjugate roots x = ±2i.
Calculation Methodology
For quadratic ax² + bx + c = 0, discriminant D = b² - 4ac dictates solutions: D > 0 yields two distinct real roots; D = 0 gives a single repeated root; D < 0 yields complex conjugate pairs.
Frequently Asked Questions
What equation classes can be solved?
Linear, quadratic, biquadratic, cubic polynomial equations, and linear systems.
What does the discriminant D indicate?
The expression D = b² - 4ac determines the quantity and nature of roots for a quadratic polynomial.
What happens when discriminant D is negative?
The equation has no real number roots, resulting instead in two complex conjugate roots involving imaginary unit i.
How to enter powers and multipliers?
Use caret ^ for powers (x^2) and asterisk * for multiplication.
Related Tools
Compound Interest Calculator
Calculate monthly investment growth with compounding interest.
Cash Loan Calculator
Calculate monthly payment, total interest, and comparison between annuity and differentiated loans.
Mortgage Early Payoff
Evaluate interest saved and mortgage term reduction with extra principal payments.
Customs Clearance Calculator (EU & USA)
Calculates vehicle customs clearance taxes in Ukraine: import duty, excise tax, VAT, and US import delivery fees.