2/y+3=y+9

Solution for 2/y+3=y+9 equation:

2/y+3=y+9

We move all terms to the left:

2/y+3-(y+9)=0


Domain of the equation: y!=0

y∈R


We get rid of parentheses

2/y-y-9+3=0

We multiply all the terms by the denominator


-y*y-9*y+3*y+2=0

We add all the numbers together, and all the variables

-6y-y*y+2=0

Wy multiply elements

-1y^2-6y+2=0

a = -1; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-1)·2
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*-1}=\frac{6-2\sqrt{11}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*-1}=\frac{6+2\sqrt{11}}{-2}
$