1/7y=1/3y+2

Solution for 1/7y=1/3y+2 equation:

1/7y=1/3y+2

We move all terms to the left:

1/7y-(1/3y+2)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 3y+2)!=0

y∈R


We get rid of parentheses

1/7y-1/3y-2=0

We calculate fractions


3y/21y^2+(-7y)/21y^2-2=0

We multiply all the terms by the denominator


3y+(-7y)-2*21y^2=0

Wy multiply elements

-42y^2+3y+(-7y)=0

We get rid of parentheses

-42y^2+3y-7y=0

We add all the numbers together, and all the variables

-42y^2-4y=0

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