X-7/5x+1=x+5/x

Solution for X-7/5x+1=x+5/x equation:

X-7/5X+1=X+5/X

We move all terms to the left:

X-7/5X+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-7/5X-(+X+5/X)+1=0

We get rid of parentheses

X-7/5X-X-5/X+1=0

We calculate fractions


X-X+(-7X)/5X^2+(-25X)/5X^2+1=0

We add all the numbers together, and all the variables

(-7X)/5X^2+(-25X)/5X^2+1=0

We multiply all the terms by the denominator


(-7X)+(-25X)+1*5X^2=0

Wy multiply elements

5X^2+(-7X)+(-25X)=0

We get rid of parentheses

5X^2-7X-25X=0

We add all the numbers together, and all the variables

5X^2-32X=0

a = 5; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·5·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*5}=\frac{0}{10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*5}=\frac{64}{10}
=6+2/5
$