1/7w-1/3=1/21w

Solution for 1/7w-1/3=1/21w equation:

1/7w-1/3=1/21w

We move all terms to the left:

1/7w-1/3-(1/21w)=0


Domain of the equation: 7w!=0

w!=0/7

w!=0

w∈R



Domain of the equation: 21w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

1/7w-(+1/21w)-1/3=0

We get rid of parentheses

1/7w-1/21w-1/3=0

We calculate fractions


(-294w^2)/1323w^2+189w/1323w^2+(-63w)/1323w^2=0

We multiply all the terms by the denominator


(-294w^2)+189w+(-63w)=0

We get rid of parentheses

-294w^2+189w-63w=0

We add all the numbers together, and all the variables

-294w^2+126w=0

a = -294; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·(-294)·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*-294}=\frac{-252}{-588}
=3/7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*-294}=\frac{0}{-588}
=0
$