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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+2x^2+6x+18x+54)), so:

(+2x^2+6x+18x+54)

We get rid of parentheses

2x^2+6x+18x+54

We add all the numbers together, and all the variables

2x^2+24x+54

Back to the equation:

-(2x^2+24x+54)


We get rid of parentheses

-2x^2-24x-54+180=0

We add all the numbers together, and all the variables

-2x^2-24x+126=0

a = -2; b = -24; c = +126;
Δ = b2-4ac
Δ = -242-4·(-2)·126
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{11}}{2*-2}=\frac{24-12\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{11}}{2*-2}=\frac{24+12\sqrt{11}}{-4}
$