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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


x-x+(-2x)/5x^2+(-15x)/5x^2+1=0

We add all the numbers together, and all the variables

(-2x)/5x^2+(-15x)/5x^2+1=0

We multiply all the terms by the denominator


(-2x)+(-15x)+1*5x^2=0

Wy multiply elements

5x^2+(-2x)+(-15x)=0

We get rid of parentheses

5x^2-2x-15x=0

We add all the numbers together, and all the variables

5x^2-17x=0

a = 5; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·5·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*5}=\frac{34}{10}
=3+2/5
$