-9-5/6w=-2/3w+3

Solution for -9-5/6w=-2/3w+3 equation:

-9-5/6w=-2/3w+3

We move all terms to the left:

-9-5/6w-(-2/3w+3)=0


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R



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

w∈R


We get rid of parentheses

-5/6w+2/3w-3-9=0

We calculate fractions


(-15w)/18w^2+12w/18w^2-3-9=0

We add all the numbers together, and all the variables

(-15w)/18w^2+12w/18w^2-12=0

We multiply all the terms by the denominator


(-15w)+12w-12*18w^2=0

We add all the numbers together, and all the variables

12w+(-15w)-12*18w^2=0

Wy multiply elements

-216w^2+12w+(-15w)=0

We get rid of parentheses

-216w^2+12w-15w=0

We add all the numbers together, and all the variables

-216w^2-3w=0

a = -216; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-216)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-216}=\frac{0}{-432}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-216}=\frac{6}{-432}
=-1/72
$