8/9y-3=2/3y+2

Solution for 8/9y-3=2/3y+2 equation:

8/9y-3=2/3y+2

We move all terms to the left:

8/9y-3-(2/3y+2)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



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

y∈R


We get rid of parentheses

8/9y-2/3y-2-3=0

We calculate fractions


24y/27y^2+(-18y)/27y^2-2-3=0

We add all the numbers together, and all the variables

24y/27y^2+(-18y)/27y^2-5=0

We multiply all the terms by the denominator


24y+(-18y)-5*27y^2=0

Wy multiply elements

-135y^2+24y+(-18y)=0

We get rid of parentheses

-135y^2+24y-18y=0

We add all the numbers together, and all the variables

-135y^2+6y=0

a = -135; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-135)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-135}=\frac{-12}{-270}
=2/45
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-135}=\frac{0}{-270}
=0
$