x-4/5x+1=x+4/x

Solution for x-4/5x+1=x+4/x equation:

x-4/5x+1=x+4/x

We move all terms to the left:

x-4/5x+1-(x+4/x)=0


Domain of the equation: 5x!=0

x!=0/5

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-4/5x-(+x+4/x)+1=0

We get rid of parentheses

x-4/5x-x-4/x+1=0

We calculate fractions


x-x+(-4x)/5x^2+(-20x)/5x^2+1=0

We add all the numbers together, and all the variables

(-4x)/5x^2+(-20x)/5x^2+1=0

We multiply all the terms by the denominator


(-4x)+(-20x)+1*5x^2=0

Wy multiply elements

5x^2+(-4x)+(-20x)=0

We get rid of parentheses

5x^2-4x-20x=0

We add all the numbers together, and all the variables

5x^2-24x=0

a = 5; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·5·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*5}=\frac{48}{10}
=4+4/5
$