1008=(2x+8)(x+6)

Solution for 1008=(2x+8)(x+6) equation:

1008=(2x+8)(x+6)

We move all terms to the left:

1008-((2x+8)(x+6))=0

We multiply parentheses ..

-((+2x^2+12x+8x+48))+1008=0


We calculate terms in parentheses: -((+2x^2+12x+8x+48)), so:

(+2x^2+12x+8x+48)

We get rid of parentheses

2x^2+12x+8x+48

We add all the numbers together, and all the variables

2x^2+20x+48

Back to the equation:

-(2x^2+20x+48)


We get rid of parentheses

-2x^2-20x-48+1008=0

We add all the numbers together, and all the variables

-2x^2-20x+960=0

a = -2; b = -20; c = +960;
Δ = b2-4ac
Δ = -202-4·(-2)·960
Δ = 8080
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:

$\sqrt{\Delta}=\sqrt{8080}=\sqrt{16*505}=\sqrt{16}*\sqrt{505}=4\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{505}}{2*-2}=\frac{20-4\sqrt{505}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{505}}{2*-2}=\frac{20+4\sqrt{505}}{-4}
$