2/15w=1+1/10w

Solution for 2/15w=1+1/10w equation:

2/15w=1+1/10w

We move all terms to the left:

2/15w-(1+1/10w)=0


Domain of the equation: 15w!=0

w!=0/15

w!=0

w∈R



Domain of the equation: 10w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2/15w-(1/10w+1)=0

We get rid of parentheses

2/15w-1/10w-1=0

We calculate fractions


20w/150w^2+(-15w)/150w^2-1=0

We multiply all the terms by the denominator


20w+(-15w)-1*150w^2=0

Wy multiply elements

-150w^2+20w+(-15w)=0

We get rid of parentheses

-150w^2+20w-15w=0

We add all the numbers together, and all the variables

-150w^2+5w=0

a = -150; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-150)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-150}=\frac{-10}{-300}
=1/30
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-150}=\frac{0}{-300}
=0
$