(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+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}
$