2/15w=1+1/9w

Solution for 2/15w=1+1/9w equation:

2/15w=1+1/9w

We move all terms to the left:

2/15w-(1+1/9w)=0


Domain of the equation: 15w!=0

w!=0/15

w!=0

w∈R



Domain of the equation: 9w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2/15w-(1/9w+1)=0

We get rid of parentheses

2/15w-1/9w-1=0

We calculate fractions


18w/135w^2+(-15w)/135w^2-1=0

We multiply all the terms by the denominator


18w+(-15w)-1*135w^2=0

Wy multiply elements

-135w^2+18w+(-15w)=0

We get rid of parentheses

-135w^2+18w-15w=0

We add all the numbers together, and all the variables

-135w^2+3w=0

a = -135; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-135)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-135}=\frac{-6}{-270}
=1/45
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-135}=\frac{0}{-270}
=0
$