Equation Solver
Solve linear equations (ax + b = 0) and quadratic equations (ax² + bx + c = 0). Enter the coefficients and get the solution instantly, including complex roots.
2x - 8 = 0
Recommended Settings
Pro Tips
- •A linear equation has exactly one solution unless a = 0, in which case it either has no solution or infinitely many
- •A quadratic equation's discriminant (b² − 4ac) determines the type of solution: positive gives two real roots, zero gives one repeated root, and negative gives two complex roots
- •If you set a = 0 in the quadratic solver, the equation becomes linear and is solved accordingly
- •Complex roots always come in a conjugate pair (the imaginary parts have opposite signs)
Most Popular
Most users solve quadratic equations to check homework or find the roots of a parabola
When to Use This Tool
Check your work on linear or quadratic equation problems.
Find the roots of a quadratic function, such as where a parabola crosses the x-axis.
Verify a hand-calculated solution to an equation before moving on to the next step of a larger problem.
See how changing coefficients affects whether a quadratic has real or complex solutions.
How It Works
For a linear equation, solve directly for x using x = −b ÷ a
For a quadratic equation, calculate the discriminant (b² − 4ac) to determine how many real solutions exist
Apply the quadratic formula, x = (−b ± √discriminant) ÷ 2a, using the appropriate branch based on the discriminant's sign
Display the result as one real solution, two real solutions, or a complex conjugate pair
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Frequently Asked Questions
What is the discriminant?
The discriminant is the value b² − 4ac from the quadratic formula. Its sign tells you what kind of solutions the equation has: positive means two real roots, zero means one repeated real root, and negative means two complex roots.
What are complex roots?
When the discriminant is negative, the square root involves a negative number, which has no real value. The solutions are expressed using the imaginary unit i (where i² = −1) as a pair of complex conjugates.
What happens if a = 0 in the quadratic solver?
The x² term disappears, so the equation becomes linear (bx + c = 0) and is solved as such, unless b is also 0, in which case the equation reduces to just a constant.
Is my data sent to a server?
No. All calculations happen instantly in your browser using JavaScript. Nothing you enter is transmitted anywhere.
Does this solve higher-degree polynomials?
No, this tool currently supports linear and quadratic equations only. Cubic and higher-degree equations require more advanced root-finding methods not covered here.