X(.5x+6)=144

Solution for X(.5x+6)=144 equation:

X(.5X+6)=144

We move all terms to the left:

X(.5X+6)-(144)=0

We multiply parentheses

X^2+6X-144=0

a = 1; b = 6; c = -144;
Δ = b2-4ac
Δ = 62-4·1·(-144)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{17}}{2*1}=\frac{-6-6\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{17}}{2*1}=\frac{-6+6\sqrt{17}}{2}
$