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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1008/2x-x-6-8=0

We multiply all the terms by the denominator


-x*2x-6*2x-8*2x+1008=0

Wy multiply elements

-2x^2-12x-16x+1008=0

We add all the numbers together, and all the variables

-2x^2-28x+1008=0

a = -2; b = -28; c = +1008;
Δ = b2-4ac
Δ = -282-4·(-2)·1008
Δ = 8848
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:

$\sqrt{\Delta}=\sqrt{8848}=\sqrt{16*553}=\sqrt{16}*\sqrt{553}=4\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{553}}{2*-2}=\frac{28-4\sqrt{553}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{553}}{2*-2}=\frac{28+4\sqrt{553}}{-4}
$