2/3y-11=8/9y+5

Solution for 2/3y-11=8/9y+5 equation:

2/3y-11=8/9y+5

We move all terms to the left:

2/3y-11-(8/9y+5)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 9y+5)!=0

y∈R


We get rid of parentheses

2/3y-8/9y-5-11=0

We calculate fractions


18y/27y^2+(-24y)/27y^2-5-11=0

We add all the numbers together, and all the variables

18y/27y^2+(-24y)/27y^2-16=0

We multiply all the terms by the denominator


18y+(-24y)-16*27y^2=0

Wy multiply elements

-432y^2+18y+(-24y)=0

We get rid of parentheses

-432y^2+18y-24y=0

We add all the numbers together, and all the variables

-432y^2-6y=0

a = -432; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-432)·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*-432}=\frac{0}{-864}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-432}=\frac{12}{-864}
=-1/72
$