1/6y-11/9y-7/9=2/3

Solution for 1/6y-11/9y-7/9=2/3 equation:

1/6y-11/9y-7/9=2/3

We move all terms to the left:

1/6y-11/9y-7/9-(2/3)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We add all the numbers together, and all the variables

1/6y-11/9y-7/9-(+2/3)=0

We get rid of parentheses

1/6y-11/9y-7/9-2/3=0

We calculate fractions


(-8748y^2)/13122y^2+2187y/13122y^2+(-594y)/13122y^2+(-378y)/13122y^2=0

We multiply all the terms by the denominator


(-8748y^2)+2187y+(-594y)+(-378y)=0

We get rid of parentheses

-8748y^2+2187y-594y-378y=0

We add all the numbers together, and all the variables

-8748y^2+1215y=0

a = -8748; b = 1215; c = 0;
Δ = b2-4ac
Δ = 12152-4·(-8748)·0
Δ = 1476225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1476225}=1215$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1215)-1215}{2*-8748}=\frac{-2430}{-17496}
=5/36
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1215)+1215}{2*-8748}=\frac{0}{-17496}
=0
$