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

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

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

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

3/4w-1/3w-16=0

We calculate fractions


9w/12w^2+(-4w)/12w^2-16=0

We multiply all the terms by the denominator


9w+(-4w)-16*12w^2=0

Wy multiply elements

-192w^2+9w+(-4w)=0

We get rid of parentheses

-192w^2+9w-4w=0

We add all the numbers together, and all the variables

-192w^2+5w=0

a = -192; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-192)·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*-192}=\frac{-10}{-384}
=5/192
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-192}=\frac{0}{-384}
=0
$