(-2/x-4)+2=x+2

Solution for (-2/x-4)+2=x+2 equation:

(-2/x-4)+2=x+2

We move all terms to the left:

(-2/x-4)+2-(x+2)=0


Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

-2/x-x-4-2+2=0

We multiply all the terms by the denominator


-x*x-4*x-2*x+2*x-2=0

We add all the numbers together, and all the variables

-4x-x*x-2=0

Wy multiply elements

-1x^2-4x-2=0

a = -1; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·(-1)·(-2)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{2}}{2*-1}=\frac{4-2\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{2}}{2*-1}=\frac{4+2\sqrt{2}}{-2}
$