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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 2w+9)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12w^2+2w+(-3w)=0

We get rid of parentheses

-12w^2+2w-3w=0

We add all the numbers together, and all the variables

-12w^2-1w=0

a = -12; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-12)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-12}=\frac{0}{-24}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-12}=\frac{2}{-24}
=-1/12
$