(3x+4)(8x-28)=108

Solution for (3x+4)(8x-28)=108 equation:

(3x+4)(8x-28)=108

We move all terms to the left:

(3x+4)(8x-28)-(108)=0

We multiply parentheses ..

(+24x^2-84x+32x-112)-108=0

We get rid of parentheses

24x^2-84x+32x-112-108=0

We add all the numbers together, and all the variables

24x^2-52x-220=0

a = 24; b = -52; c = -220;
Δ = b2-4ac
Δ = -522-4·24·(-220)
Δ = 23824
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:

$\sqrt{\Delta}=\sqrt{23824}=\sqrt{16*1489}=\sqrt{16}*\sqrt{1489}=4\sqrt{1489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{1489}}{2*24}=\frac{52-4\sqrt{1489}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{1489}}{2*24}=\frac{52+4\sqrt{1489}}{48}
$