3-2/9w=1/3w-7

Solution for 3-2/9w=1/3w-7 equation:

3-2/9w=1/3w-7

We move all terms to the left:

3-2/9w-(1/3w-7)=0


Domain of the equation: 9w!=0

w!=0/9

w!=0

w∈R



Domain of the equation: 3w-7)!=0

w∈R


We get rid of parentheses

-2/9w-1/3w+7+3=0

We calculate fractions


(-6w)/27w^2+(-9w)/27w^2+7+3=0

We add all the numbers together, and all the variables

(-6w)/27w^2+(-9w)/27w^2+10=0

We multiply all the terms by the denominator


(-6w)+(-9w)+10*27w^2=0

Wy multiply elements

270w^2+(-6w)+(-9w)=0

We get rid of parentheses

270w^2-6w-9w=0

We add all the numbers together, and all the variables

270w^2-15w=0

a = 270; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·270·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*270}=\frac{0}{540}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*270}=\frac{30}{540}
=1/18
$