4/2x=8/x+2

Solution for 4/2x=8/x+2 equation:

4/2x=8/x+2

We move all terms to the left:

4/2x-(8/x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

4/2x-8/x-2=0

We calculate fractions


4x/2x^2+(-16x)/2x^2-2=0

We multiply all the terms by the denominator


4x+(-16x)-2*2x^2=0

Wy multiply elements

-4x^2+4x+(-16x)=0

We get rid of parentheses

-4x^2+4x-16x=0

We add all the numbers together, and all the variables

-4x^2-12x=0

a = -4; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-4)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-4}=\frac{24}{-8}
=-3
$