X(x+12)48=180

Solution for X(x+12)48=180 equation:

X(X+12)48=180

We move all terms to the left:

X(X+12)48-(180)=0

We multiply parentheses

48X^2+576X-180=0

a = 48; b = 576; c = -180;
Δ = b2-4ac
Δ = 5762-4·48·(-180)
Δ = 366336
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:

$\sqrt{\Delta}=\sqrt{366336}=\sqrt{2304*159}=\sqrt{2304}*\sqrt{159}=48\sqrt{159}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-48\sqrt{159}}{2*48}=\frac{-576-48\sqrt{159}}{96}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+48\sqrt{159}}{2*48}=\frac{-576+48\sqrt{159}}{96}
$