Quadratic Equation Solver

If you have an equation of the form "ax2 + bx + c = 0", we can solve it for you.
Just enter the values of a, b and c below

Is it Quadratic?

Quadratic Equation

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

The "±" means you 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. If it is positive, you will get two real solutions, if it is zero you get just ONE solution, and if it is negative you get complex solutions.


Note: you can still access the old version here.