3/w=4/3w+6

Solution for 3/w=4/3w+6 equation:

3/w=4/3w+6

We move all terms to the left:

3/w-(4/3w+6)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 3w+6)!=0

w∈R


We get rid of parentheses

3/w-4/3w-6=0

We calculate fractions


9w/3w^2+(-4w)/3w^2-6=0

We multiply all the terms by the denominator


9w+(-4w)-6*3w^2=0

Wy multiply elements

-18w^2+9w+(-4w)=0

We get rid of parentheses

-18w^2+9w-4w=0

We add all the numbers together, and all the variables

-18w^2+5w=0

a = -18; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-18)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-18}=\frac{-10}{-36}
=5/18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-18}=\frac{0}{-36}
=0
$