x-5/3x+2=x+1/x

Solution for x-5/3x+2=x+1/x equation:

x-5/3x+2=x+1/x

We move all terms to the left:

x-5/3x+2-(x+1/x)=0


Domain of the equation: 3x!=0

x!=0/3

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-5/3x-(+x+1/x)+2=0

We get rid of parentheses

x-5/3x-x-1/x+2=0

We calculate fractions


x-x+(-5x)/3x^2+(-3x)/3x^2+2=0

We add all the numbers together, and all the variables

(-5x)/3x^2+(-3x)/3x^2+2=0

We multiply all the terms by the denominator


(-5x)+(-3x)+2*3x^2=0

Wy multiply elements

6x^2+(-5x)+(-3x)=0

We get rid of parentheses

6x^2-5x-3x=0

We add all the numbers together, and all the variables

6x^2-8x=0

a = 6; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·6·0
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*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*6}=\frac{16}{12}
=1+1/3
$