2/3y+1/9y+11/9=13/6

Solution for 2/3y+1/9y+11/9=13/6 equation:

2/3y+1/9y+11/9=13/6

We move all terms to the left:

2/3y+1/9y+11/9-(13/6)=0


Domain of the equation: 3y!=0

y!=0/3

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

2/3y+1/9y+11/9-(+13/6)=0

We get rid of parentheses

2/3y+1/9y+11/9-13/6=0

We calculate fractions


(-28431y^2)/13122y^2+8748y/13122y^2+108y/13122y^2+1188y/13122y^2=0

We multiply all the terms by the denominator


(-28431y^2)+8748y+108y+1188y=0

We add all the numbers together, and all the variables

(-28431y^2)+10044y=0

We get rid of parentheses

-28431y^2+10044y=0

a = -28431; b = 10044; c = 0;
Δ = b2-4ac
Δ = 100442-4·(-28431)·0
Δ = 100881936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100881936}=10044$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10044)-10044}{2*-28431}=\frac{-20088}{-56862}
=124/351
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10044)+10044}{2*-28431}=\frac{0}{-56862}
=0
$