2y-5=5/y

Solution for 2y-5=5/y equation:

2y-5=5/y

We move all terms to the left:

2y-5-(5/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2y-(+5/y)-5=0

We get rid of parentheses

2y-5/y-5=0

We multiply all the terms by the denominator


2y*y-5*y-5=0

We add all the numbers together, and all the variables

-5y+2y*y-5=0

Wy multiply elements

2y^2-5y-5=0

a = 2; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·2·(-5)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{65}}{2*2}=\frac{5-\sqrt{65}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*2}=\frac{5+\sqrt{65}}{4}
$