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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+2x^2+16x-6x-48))+1008=0


We calculate terms in parentheses: -((+2x^2+16x-6x-48)), so:

(+2x^2+16x-6x-48)

We get rid of parentheses

2x^2+16x-6x-48

We add all the numbers together, and all the variables

2x^2+10x-48

Back to the equation:

-(2x^2+10x-48)


We get rid of parentheses

-2x^2-10x+48+1008=0

We add all the numbers together, and all the variables

-2x^2-10x+1056=0

a = -2; b = -10; c = +1056;
Δ = b2-4ac
Δ = -102-4·(-2)·1056
Δ = 8548
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:

$\sqrt{\Delta}=\sqrt{8548}=\sqrt{4*2137}=\sqrt{4}*\sqrt{2137}=2\sqrt{2137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{2137}}{2*-2}=\frac{10-2\sqrt{2137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{2137}}{2*-2}=\frac{10+2\sqrt{2137}}{-4}
$