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

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

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

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 2y+2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


2y/12y^2+(-6y)/12y^2-2+1=0

We add all the numbers together, and all the variables

2y/12y^2+(-6y)/12y^2-1=0

We multiply all the terms by the denominator


2y+(-6y)-1*12y^2=0

Wy multiply elements

-12y^2+2y+(-6y)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-12y^2-4y=0

a = -12; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-12}=\frac{0}{-24}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-12}=\frac{8}{-24}
=-1/3
$