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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


x-x+(-5x)/5x^2+(-25x)/5x^2+1=0

We add all the numbers together, and all the variables

(-5x)/5x^2+(-25x)/5x^2+1=0

We multiply all the terms by the denominator


(-5x)+(-25x)+1*5x^2=0

Wy multiply elements

5x^2+(-5x)+(-25x)=0

We get rid of parentheses

5x^2-5x-25x=0

We add all the numbers together, and all the variables

5x^2-30x=0

a = 5; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·5·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*5}=\frac{60}{10}
=6
$