9=y+1/5y

Solution for 9=y+1/5y equation:

9=y+1/5y

We move all terms to the left:

9-(y+1/5y)=0


Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-(+y+1/5y)+9=0

We get rid of parentheses

-y-1/5y+9=0

We multiply all the terms by the denominator


-y*5y+9*5y-1=0

Wy multiply elements

-5y^2+45y-1=0

a = -5; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·(-5)·(-1)
Δ = 2005
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{-(45)-\sqrt{2005}}{2*-5}=\frac{-45-\sqrt{2005}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2005}}{2*-5}=\frac{-45+\sqrt{2005}}{-10}
$