(4x+12)(2x+24)=180

Solution for (4x+12)(2x+24)=180 equation:

(4x+12)(2x+24)=180

We move all terms to the left:

(4x+12)(2x+24)-(180)=0

We multiply parentheses ..

(+8x^2+96x+24x+288)-180=0

We get rid of parentheses

8x^2+96x+24x+288-180=0

We add all the numbers together, and all the variables

8x^2+120x+108=0

a = 8; b = 120; c = +108;
Δ = b2-4ac
Δ = 1202-4·8·108
Δ = 10944
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:

$\sqrt{\Delta}=\sqrt{10944}=\sqrt{576*19}=\sqrt{576}*\sqrt{19}=24\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{19}}{2*8}=\frac{-120-24\sqrt{19}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{19}}{2*8}=\frac{-120+24\sqrt{19}}{16}
$