3/2y+5=-1/3y

Solution for 3/2y+5=-1/3y equation:

3/2y+5=-1/3y

We move all terms to the left:

3/2y+5-(-1/3y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

3/2y+1/3y+5=0

We calculate fractions


9y/6y^2+2y/6y^2+5=0

We multiply all the terms by the denominator


9y+2y+5*6y^2=0

We add all the numbers together, and all the variables

11y+5*6y^2=0

Wy multiply elements

30y^2+11y=0

a = 30; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·30·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*30}=\frac{-22}{60}
=-11/30
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*30}=\frac{0}{60}
=0
$