(2x+20)(6x+24)=180

Solution for (2x+20)(6x+24)=180 equation:

(2x+20)(6x+24)=180

We move all terms to the left:

(2x+20)(6x+24)-(180)=0

We multiply parentheses ..

(+12x^2+48x+120x+480)-180=0

We get rid of parentheses

12x^2+48x+120x+480-180=0

We add all the numbers together, and all the variables

12x^2+168x+300=0

a = 12; b = 168; c = +300;
Δ = b2-4ac
Δ = 1682-4·12·300
Δ = 13824
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:

$\sqrt{\Delta}=\sqrt{13824}=\sqrt{2304*6}=\sqrt{2304}*\sqrt{6}=48\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-48\sqrt{6}}{2*12}=\frac{-168-48\sqrt{6}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+48\sqrt{6}}{2*12}=\frac{-168+48\sqrt{6}}{24}
$