2/2x-8=5/x+4

Solution for 2/2x-8=5/x+4 equation:

2/2x-8=5/x+4

We move all terms to the left:

2/2x-8-(5/x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/2x-5/x-4-8=0

We calculate fractions


2x/2x^2+(-10x)/2x^2-4-8=0

We add all the numbers together, and all the variables

2x/2x^2+(-10x)/2x^2-12=0

We multiply all the terms by the denominator


2x+(-10x)-12*2x^2=0

Wy multiply elements

-24x^2+2x+(-10x)=0

We get rid of parentheses

-24x^2+2x-10x=0

We add all the numbers together, and all the variables

-24x^2-8x=0

a = -24; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-24)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-24}=\frac{16}{-48}
=-1/3
$