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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y-2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


(-81y)/108y^2+4y/108y^2+8y/108y^2+2=0

We multiply all the terms by the denominator


(-81y)+4y+8y+2*108y^2=0

We add all the numbers together, and all the variables

12y+(-81y)+2*108y^2=0

Wy multiply elements

216y^2+12y+(-81y)=0

We get rid of parentheses

216y^2+12y-81y=0

We add all the numbers together, and all the variables

216y^2-69y=0

a = 216; b = -69; c = 0;
Δ = b2-4ac
Δ = -692-4·216·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-69}{2*216}=\frac{0}{432}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+69}{2*216}=\frac{138}{432}
=23/72
$