2/3w+4=2/5w

Solution for 2/3w+4=2/5w equation:

2/3w+4=2/5w

We move all terms to the left:

2/3w+4-(2/5w)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2/3w-(+2/5w)+4=0

We get rid of parentheses

2/3w-2/5w+4=0

We calculate fractions


10w/15w^2+(-6w)/15w^2+4=0

We multiply all the terms by the denominator


10w+(-6w)+4*15w^2=0

Wy multiply elements

60w^2+10w+(-6w)=0

We get rid of parentheses

60w^2+10w-6w=0

We add all the numbers together, and all the variables

60w^2+4w=0

a = 60; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·60·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*60}=\frac{-8}{120}
=-1/15
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*60}=\frac{0}{120}
=0
$