3/4w=1/5w+44

Solution for 3/4w=1/5w+44 equation:

3/4w=1/5w+44

We move all terms to the left:

3/4w-(1/5w+44)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 5w+44)!=0

w∈R


We get rid of parentheses

3/4w-1/5w-44=0

We calculate fractions


15w/20w^2+(-4w)/20w^2-44=0

We multiply all the terms by the denominator


15w+(-4w)-44*20w^2=0

Wy multiply elements

-880w^2+15w+(-4w)=0

We get rid of parentheses

-880w^2+15w-4w=0

We add all the numbers together, and all the variables

-880w^2+11w=0

a = -880; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-880)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-880}=\frac{-22}{-1760}
=1/80
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-880}=\frac{0}{-1760}
=0
$