1/3w-1/2w-4=12

Solution for 1/3w-1/2w-4=12 equation:

1/3w-1/2w-4=12

We move all terms to the left:

1/3w-1/2w-4-(12)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

1/3w-1/2w-16=0

We calculate fractions


2w/6w^2+(-3w)/6w^2-16=0

We multiply all the terms by the denominator


2w+(-3w)-16*6w^2=0

Wy multiply elements

-96w^2+2w+(-3w)=0

We get rid of parentheses

-96w^2+2w-3w=0

We add all the numbers together, and all the variables

-96w^2-1w=0

a = -96; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-96)·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*-96}=\frac{0}{-192}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-96}=\frac{2}{-192}
=-1/96
$