1/2w-1/9=1/3w

Solution for 1/2w-1/9=1/3w equation:

1/2w-1/9=1/3w

We move all terms to the left:

1/2w-1/9-(1/3w)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

1/2w-(+1/3w)-1/9=0

We get rid of parentheses

1/2w-1/3w-1/9=0

We calculate fractions


(-18w^2)/486w^2+243w/486w^2+(-162w)/486w^2=0

We multiply all the terms by the denominator


(-18w^2)+243w+(-162w)=0

We get rid of parentheses

-18w^2+243w-162w=0

We add all the numbers together, and all the variables

-18w^2+81w=0

a = -18; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-18)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-18}=\frac{-162}{-36}
=4+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-18}=\frac{0}{-36}
=0
$