(5/y+2)=3y

Solution for (5/y+2)=3y equation:

(5/y+2)=3y

We move all terms to the left:

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


Domain of the equation: y+2)!=0

y∈R


We add all the numbers together, and all the variables

-3y+(5/y+2)=0

We get rid of parentheses

-3y+5/y+2=0

We multiply all the terms by the denominator


-3y*y+2*y+5=0

We add all the numbers together, and all the variables

2y-3y*y+5=0

Wy multiply elements

-3y^2+2y+5=0

a = -3; b = 2; c = +5;
Δ = b2-4ac
Δ = 22-4·(-3)·5
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{-(2)-8}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*-3}=\frac{6}{-6}
=-1
$