1/3w+4/5w=1/15

Solution for 1/3w+4/5w=1/15 equation:

1/3w+4/5w=1/15

We move all terms to the left:

1/3w+4/5w-(1/15)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We add all the numbers together, and all the variables

1/3w+4/5w-(+1/15)=0

We get rid of parentheses

1/3w+4/5w-1/15=0

We calculate fractions


(-75w^2)/225w^2+75w/225w^2+180w/225w^2=0

We multiply all the terms by the denominator


(-75w^2)+75w+180w=0

We add all the numbers together, and all the variables

(-75w^2)+255w=0

We get rid of parentheses

-75w^2+255w=0

a = -75; b = 255; c = 0;
Δ = b2-4ac
Δ = 2552-4·(-75)·0
Δ = 65025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65025}=255$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(255)-255}{2*-75}=\frac{-510}{-150}
=3+2/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(255)+255}{2*-75}=\frac{0}{-150}
=0
$