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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y+1/6y+2=0

We calculate fractions


6y/12y^2+2y/12y^2+2=0

We multiply all the terms by the denominator


6y+2y+2*12y^2=0

We add all the numbers together, and all the variables

8y+2*12y^2=0

Wy multiply elements

24y^2+8y=0

a = 24; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·24·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*24}=\frac{-16}{48}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*24}=\frac{0}{48}
=0
$