(4x+6)(8x+12)=120

Solution for (4x+6)(8x+12)=120 equation:

(4x+6)(8x+12)=120

We move all terms to the left:

(4x+6)(8x+12)-(120)=0

We multiply parentheses ..

(+32x^2+48x+48x+72)-120=0

We get rid of parentheses

32x^2+48x+48x+72-120=0

We add all the numbers together, and all the variables

32x^2+96x-48=0

a = 32; b = 96; c = -48;
Δ = b2-4ac
Δ = 962-4·32·(-48)
Δ = 15360
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:

$\sqrt{\Delta}=\sqrt{15360}=\sqrt{1024*15}=\sqrt{1024}*\sqrt{15}=32\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-32\sqrt{15}}{2*32}=\frac{-96-32\sqrt{15}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+32\sqrt{15}}{2*32}=\frac{-96+32\sqrt{15}}{64}
$