Quadratic Equation Solver
We can help you solve an equation of the form "ax2 + bx + c = 0"
Just enter the
values of a, b and c below:
algebra/images/quadratic-solver.js
Is it Quadratic?
Only if it can be put in the form ax2 + bx + c = 0, and a is not zero.
The name comes from "quad" meaning square, as the variable is squared (in other words x2).
These are all quadratic equations in disguise:
| In disguise | In standard form | a, b and c |
|---|---|---|
| x2 = 3x -1 | x2 - 3x + 1 = 0 | a=1, b=-3, c=1 |
| 2(x2 - 2x) = 5 | 2x2 - 4x - 5 = 0 | a=2, b=-4, c=-5 |
| x(x-1) = 3 | x2 - x - 3 = 0 | a=1, b=-1, c=-3 |
| 5 + 1/x - 1/x2 = 0 | 5x2 + x - 1 = 0 | a=5, b=1, c=-1 |
How Does this Work?
The solution(s) to a quadratic equation can be calculated using the Quadratic Formula:
![x = [ -b plus minus square root of (b^2-4ac) ] / 2a](algebra/images/quadratic-formula.svg)
The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !
The blue part (b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer:
- when it is positive, we get two real solutions,
- when it is zero we get just ONE solution,
- when it is negative we get complex solutions.
Learn more at Quadratic Equations