1/2y+1=1/6y+8

Solution for 1/2y+1=1/6y+8 equation:

1/2y+1=1/6y+8

We move all terms to the left:

1/2y+1-(1/6y+8)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 6y+8)!=0

y∈R


We get rid of parentheses

1/2y-1/6y-8+1=0

We calculate fractions


6y/12y^2+(-2y)/12y^2-8+1=0

We add all the numbers together, and all the variables

6y/12y^2+(-2y)/12y^2-7=0

We multiply all the terms by the denominator


6y+(-2y)-7*12y^2=0

Wy multiply elements

-84y^2+6y+(-2y)=0

We get rid of parentheses

-84y^2+6y-2y=0

We add all the numbers together, and all the variables

-84y^2+4y=0

a = -84; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-84)·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*-84}=\frac{-8}{-168}
=1/21
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-84}=\frac{0}{-168}
=0
$