(6x+2)(x+18)=180

Solution for (6x+2)(x+18)=180 equation:

(6x+2)(x+18)=180

We move all terms to the left:

(6x+2)(x+18)-(180)=0

We multiply parentheses ..

(+6x^2+108x+2x+36)-180=0

We get rid of parentheses

6x^2+108x+2x+36-180=0

We add all the numbers together, and all the variables

6x^2+110x-144=0

a = 6; b = 110; c = -144;
Δ = b2-4ac
Δ = 1102-4·6·(-144)
Δ = 15556
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:

$\sqrt{\Delta}=\sqrt{15556}=\sqrt{4*3889}=\sqrt{4}*\sqrt{3889}=2\sqrt{3889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{3889}}{2*6}=\frac{-110-2\sqrt{3889}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{3889}}{2*6}=\frac{-110+2\sqrt{3889}}{12}
$