1/3w-1/5=1/15w;w=15

Solution for 1/3w-1/5=1/15w;w=15 equation:

1/3w-1/5=1/15ww=15

We move all terms to the left:

1/3w-1/5-(1/15ww)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 15ww)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

1/3w-(+1/15ww)-1/5=0

We get rid of parentheses

1/3w-1/15ww-1/5=0

We calculate fractions


(-45w^2)/1125w^2+375w/1125w^2+(-75w)/1125w^2=0

We multiply all the terms by the denominator


(-45w^2)+375w+(-75w)=0

We get rid of parentheses

-45w^2+375w-75w=0

We add all the numbers together, and all the variables

-45w^2+300w=0

a = -45; b = 300; c = 0;
Δ = b2-4ac
Δ = 3002-4·(-45)·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-300}{2*-45}=\frac{-600}{-90}
=6+2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+300}{2*-45}=\frac{0}{-90}
=0
$