2y+9=y+9+16/y

Solution for 2y+9=y+9+16/y equation:

2y+9=y+9+16/y

We move all terms to the left:

2y+9-(y+9+16/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-(y+16/y+9)+9=0

We get rid of parentheses

2y-y-16/y-9+9=0

We multiply all the terms by the denominator


2y*y-y*y-9*y+9*y-16=0

We add all the numbers together, and all the variables

2y*y-y*y-16=0

Wy multiply elements

2y^2-1y^2-16=0

We add all the numbers together, and all the variables

y^2-16=0

a = 1; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1·(-16)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*1}=\frac{-8}{2}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*1}=\frac{8}{2}
=4
$