9/5w=3/w-6

Solution for 9/5w=3/w-6 equation:

9/5w=3/w-6

We move all terms to the left:

9/5w-(3/w-6)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: w-6)!=0

w∈R


We get rid of parentheses

9/5w-3/w+6=0

We calculate fractions


9w/5w^2+(-15w)/5w^2+6=0

We multiply all the terms by the denominator


9w+(-15w)+6*5w^2=0

Wy multiply elements

30w^2+9w+(-15w)=0

We get rid of parentheses

30w^2+9w-15w=0

We add all the numbers together, and all the variables

30w^2-6w=0

a = 30; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·30·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*30}=\frac{0}{60}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*30}=\frac{12}{60}
=1/5
$