3/2*y=16/y+2

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

3/2y=16/y+2

We move all terms to the left:

3/2y-(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

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4y^2-29y=0

a = -4; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-4)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-4}=\frac{0}{-8}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-4}=\frac{58}{-8}
=-7+1/4
$