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
:


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 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:

Learn more at Quadratic Equations

 

Note: you can still access the old version here.