1/2y+2+12=1/3y+8

Solution for 1/2y+2+12=1/3y+8 equation:

1/2y+2+12=1/3y+8

We move all terms to the left:

1/2y+2+12-(1/3y+8)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y+8)!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(1/3y+8)+14=0

We get rid of parentheses

1/2y-1/3y-8+14=0

We calculate fractions


3y/6y^2+(-2y)/6y^2-8+14=0

We add all the numbers together, and all the variables

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
$