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

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

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

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

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

We calculate fractions


3w/4w^2+(-4w)/4w^2-16=0

We multiply all the terms by the denominator


3w+(-4w)-16*4w^2=0

Wy multiply elements

-64w^2+3w+(-4w)=0

We get rid of parentheses

-64w^2+3w-4w=0

We add all the numbers together, and all the variables

-64w^2-1w=0

a = -64; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-64)·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*-64}=\frac{0}{-128}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-64}=\frac{2}{-128}
=-1/64
$