(1)/(3)y-(1)/(2)=(1)/(6)y

Solution for (1)/(3)y-(1)/(2)=(1)/(6)y equation:

(1)/(3)y-(1)/(2)=(1)/(6)y

We move all terms to the left:

(1)/(3)y-(1)/(2)-((1)/(6)y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3y-1/6y-1/2=0

We calculate fractions


(-108y^2)/72y^2+24y/72y^2+(-12y)/72y^2=0

We multiply all the terms by the denominator


(-108y^2)+24y+(-12y)=0

We get rid of parentheses

-108y^2+24y-12y=0

We add all the numbers together, and all the variables

-108y^2+12y=0

a = -108; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-108)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-108}=\frac{-24}{-216}
=1/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-108}=\frac{0}{-216}
=0
$