(3x+12)(2X+8)=180

Solution for (3x+12)(2X+8)=180 equation:

(3x+12)(2x+8)=180

We move all terms to the left:

(3x+12)(2x+8)-(180)=0

We multiply parentheses ..

(+6x^2+24x+24x+96)-180=0

We get rid of parentheses

6x^2+24x+24x+96-180=0

We add all the numbers together, and all the variables

6x^2+48x-84=0

a = 6; b = 48; c = -84;
Δ = b2-4ac
Δ = 482-4·6·(-84)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{30}}{2*6}=\frac{-48-12\sqrt{30}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{30}}{2*6}=\frac{-48+12\sqrt{30}}{12}
$