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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-8x)+(-8x)+5*2x^2=0

Wy multiply elements

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

We get rid of parentheses

10x^2-8x-8x=0

We add all the numbers together, and all the variables

10x^2-16x=0

a = 10; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·10·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*10}=\frac{32}{20}
=1+3/5
$