X(2x-12)+30=180

Solution for X(2x-12)+30=180 equation:

X(2X-12)+30=180

We move all terms to the left:

X(2X-12)+30-(180)=0

We add all the numbers together, and all the variables

X(2X-12)-150=0

We multiply parentheses

2X^2-12X-150=0

a = 2; b = -12; c = -150;
Δ = b2-4ac
Δ = -122-4·2·(-150)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{21}}{2*2}=\frac{12-8\sqrt{21}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{21}}{2*2}=\frac{12+8\sqrt{21}}{4}
$