1/2y-1/3y=6

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

1/2y-1/3y=6

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We calculate fractions


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

We multiply all the terms by the denominator


3y+(-2y)-6*6y^2=0

Wy multiply elements

-36y^2+3y+(-2y)=0

We get rid of parentheses

-36y^2+3y-2y=0

We add all the numbers together, and all the variables

-36y^2+y=0

a = -36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-36)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-36}=\frac{-2}{-72}
=1/36
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-36}=\frac{0}{-72}
=0
$