120=x(x+8)

Solution for 120=x(x+8) equation:

120=x(x+8)

We move all terms to the left:

120-(x(x+8))=0


We calculate terms in parentheses: -(x(x+8)), so:

x(x+8)

We multiply parentheses

x^2+8x

Back to the equation:

-(x^2+8x)


We get rid of parentheses

-x^2-8x+120=0

We add all the numbers together, and all the variables

-1x^2-8x+120=0

a = -1; b = -8; c = +120;
Δ = b2-4ac
Δ = -82-4·(-1)·120
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{34}}{2*-1}=\frac{8-4\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{34}}{2*-1}=\frac{8+4\sqrt{34}}{-2}
$