(2x+6)(x-9)=180

Solution for (2x+6)(x-9)=180 equation:

(2x+6)(x-9)=180

We move all terms to the left:

(2x+6)(x-9)-(180)=0

We multiply parentheses ..

(+2x^2-18x+6x-54)-180=0

We get rid of parentheses

2x^2-18x+6x-54-180=0

We add all the numbers together, and all the variables

2x^2-12x-234=0

a = 2; b = -12; c = -234;
Δ = b2-4ac
Δ = -122-4·2·(-234)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{14}}{2*2}=\frac{12-12\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{14}}{2*2}=\frac{12+12\sqrt{14}}{4}
$