Equation Solver
Effortlessly solve linear and quadratic equations.
Solve for x in: ax + b = c
About This Calculator
The Equation Solver helps you solve linear and quadratic equations instantly. Simply enter the coefficients of your equation, and the calculator will provide the solution with detailed steps.
Perfect for students learning algebra, engineers solving mathematical problems, or anyone who needs to find the roots of equations quickly and accurately.
Formula & Calculation Method
Equation Solving Formulas:
Linear Equation: ax + b = c
Solution: x = (c - b) / a
Quadratic Equation: ax² + bx + c = 0
Quadratic Formula:
x = (-b ± √(b² - 4ac)) / 2a
Discriminant: Δ = b² - 4ac
- If Δ > 0: Two real roots
- If Δ = 0: One real root (repeated)
- If Δ < 0: Two complex roots
How to Use This Calculator
- Select Equation Type: Choose between Linear or Quadratic equation using the tabs.
- Enter Coefficients: Input the values for a, b, and c in the input fields.
- View Solution: The solution will appear automatically below as you enter values.
- View Graph: For valid equations, see the visual representation of the equation.
- Use Features: Copy or share your result, get AI explanations, or analyze the graph.
Frequently Asked Questions
What is a linear equation?
A linear equation is of the form ax + b = c, where a, b, and c are constants and a ≠ 0. It has exactly one solution.
What is a quadratic equation?
A quadratic equation is of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. It can have 0, 1, or 2 real solutions, or 2 complex solutions.
What does the discriminant tell us?
The discriminant (b² - 4ac) determines the nature of roots: positive = two real roots, zero = one repeated root, negative = two complex roots.
Can I solve equations with complex coefficients?
The calculator supports complex solutions for quadratic equations when the discriminant is negative, showing results in the form a ± bi.
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Prof. Emily Watson, PhD
PhD in Applied MathematicsStatistics Certification
Professor Emily Watson holds a PhD in Applied Mathematics and has taught at leading universities for over 20 years. Her research focuses on making complex mathematical concepts accessible to everyone through practical applications and tools.