2/5w-1/3w=3

Solution for 2/5w-1/3w=3 equation:

2/5w-1/3w=3

We move all terms to the left:

2/5w-1/3w-(3)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We calculate fractions


6w/15w^2+(-5w)/15w^2-3=0

We multiply all the terms by the denominator


6w+(-5w)-3*15w^2=0

Wy multiply elements

-45w^2+6w+(-5w)=0

We get rid of parentheses

-45w^2+6w-5w=0

We add all the numbers together, and all the variables

-45w^2+w=0

a = -45; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-45)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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