1/3w-5=4/5w

Solution for 1/3w-5=4/5w equation:

1/3w-5=4/5w

We move all terms to the left:

1/3w-5-(4/5w)=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

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

We get rid of parentheses

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

We calculate fractions


5w/15w^2+(-12w)/15w^2-5=0

We multiply all the terms by the denominator


5w+(-12w)-5*15w^2=0

Wy multiply elements

-75w^2+5w+(-12w)=0

We get rid of parentheses

-75w^2+5w-12w=0

We add all the numbers together, and all the variables

-75w^2-7w=0

a = -75; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-75)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-75}=\frac{0}{-150}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-75}=\frac{14}{-150}
=-7/75
$