1/3y-2=2/9y+4

Solution for 1/3y-2=2/9y+4 equation:

1/3y-2=2/9y+4

We move all terms to the left:

1/3y-2-(2/9y+4)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 9y+4)!=0

y∈R


We get rid of parentheses

1/3y-2/9y-4-2=0

We calculate fractions


9y/27y^2+(-6y)/27y^2-4-2=0

We add all the numbers together, and all the variables

9y/27y^2+(-6y)/27y^2-6=0

We multiply all the terms by the denominator


9y+(-6y)-6*27y^2=0

Wy multiply elements

-162y^2+9y+(-6y)=0

We get rid of parentheses

-162y^2+9y-6y=0

We add all the numbers together, and all the variables

-162y^2+3y=0

a = -162; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-162)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-162}=\frac{-6}{-324}
=1/54
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-162}=\frac{0}{-324}
=0
$