1/y+1=1/6y

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

1/y+1=1/6y

We move all terms to the left:

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


Domain of the equation: 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/y-(+1/6y)+1=0

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6y^2+5y=0

a = 6; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·6·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*6}=\frac{-10}{12}
=-5/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*6}=\frac{0}{12}
=0
$