X(0.5x+12)=1080

Solution for X(0.5x+12)=1080 equation:

X(0.5X+12)=1080

We move all terms to the left:

X(0.5X+12)-(1080)=0

We multiply parentheses

0X^2+12X-1080=0

We add all the numbers together, and all the variables

X^2+12X-1080=0

a = 1; b = 12; c = -1080;
Δ = b2-4ac
Δ = 122-4·1·(-1080)
Δ = 4464
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:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{31}}{2*1}=\frac{-12-12\sqrt{31}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{31}}{2*1}=\frac{-12+12\sqrt{31}}{2}
$