X(2x+6)+54=180

Solution for X(2x+6)+54=180 equation:

X(2X+6)+54=180

We move all terms to the left:

X(2X+6)+54-(180)=0

We add all the numbers together, and all the variables

X(2X+6)-126=0

We multiply parentheses

2X^2+6X-126=0

a = 2; b = 6; c = -126;
Δ = b2-4ac
Δ = 62-4·2·(-126)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{29}}{2*2}=\frac{-6-6\sqrt{29}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{29}}{2*2}=\frac{-6+6\sqrt{29}}{4}
$