2/3y+3/2=-1/12y

Solution for 2/3y+3/2=-1/12y equation:

2/3y+3/2=-1/12y

We move all terms to the left:

2/3y+3/2-(-1/12y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 12y)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

2/3y+1/12y+3/2=0

We calculate fractions


108y^2/144y^2+96y/144y^2+12y/144y^2=0

We multiply all the terms by the denominator


108y^2+96y+12y=0

We add all the numbers together, and all the variables

108y^2+108y=0

a = 108; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·108·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*108}=\frac{-216}{216}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*108}=\frac{0}{216}
=0
$