20/9w-8=4/w

Solution for 20/9w-8=4/w equation:

20/9w-8=4/w

We move all terms to the left:

20/9w-8-(4/w)=0


Domain of the equation: 9w!=0

w!=0/9

w!=0

w∈R



Domain of the equation: w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

20/9w-(+4/w)-8=0

We get rid of parentheses

20/9w-4/w-8=0

We calculate fractions


20w/9w^2+(-36w)/9w^2-8=0

We multiply all the terms by the denominator


20w+(-36w)-8*9w^2=0

Wy multiply elements

-72w^2+20w+(-36w)=0

We get rid of parentheses

-72w^2+20w-36w=0

We add all the numbers together, and all the variables

-72w^2-16w=0

a = -72; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-72)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-72}=\frac{0}{-144}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-72}=\frac{32}{-144}
=-2/9
$