x(x+-4)=120

Solution for x(x+-4)=120 equation:

x(x+-4)=120

We move all terms to the left:

x(x+-4)-(120)=0

We add all the numbers together, and all the variables

x(x-4)-120=0

We multiply parentheses

x^2-4x-120=0

a = 1; b = -4; c = -120;
Δ = b2-4ac
Δ = -42-4·1·(-120)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{31}}{2*1}=\frac{4-4\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{31}}{2*1}=\frac{4+4\sqrt{31}}{2}
$