3y/2y=16/y+2

Solution for 3y/2y=16/y+2 equation:

3y/2y=16/y+2

We move all terms to the left:

3y/2y-(16/y+2)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

3y/2y-16/y-2=0

We calculate fractions


3y^2/2y^2+(-32y)/2y^2-2=0

We multiply all the terms by the denominator


3y^2+(-32y)-2*2y^2=0

Wy multiply elements

3y^2-4y^2+(-32y)=0

We get rid of parentheses

3y^2-4y^2-32y=0

We add all the numbers together, and all the variables

-1y^2-32y=0

a = -1; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-1)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-1}=\frac{0}{-2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-1}=\frac{64}{-2}
=-32
$