3/3-3/2y=-1/3y-4

Solution for 3/3-3/2y=-1/3y-4 equation:

3/3-3/2y=-1/3y-4

We move all terms to the left:

3/3-3/2y-(-1/3y-4)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y-4)!=0

y∈R


We add all the numbers together, and all the variables

-3/2y-(-1/3y-4)+1=0

We get rid of parentheses

-3/2y+1/3y+4+1=0

We calculate fractions


(-9y)/6y^2+2y/6y^2+4+1=0

We add all the numbers together, and all the variables

(-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

2y+(-9y)+5*6y^2=0

Wy multiply elements

30y^2+2y+(-9y)=0

We get rid of parentheses

30y^2+2y-9y=0

We add all the numbers together, and all the variables

30y^2-7y=0

a = 30; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·30·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*30}=\frac{0}{60}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*30}=\frac{14}{60}
=7/30
$