3/4w-12=3/2w

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

3/4w-12=3/2w

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/4w-3/2w-12=0

We calculate fractions


6w/8w^2+(-12w)/8w^2-12=0

We multiply all the terms by the denominator


6w+(-12w)-12*8w^2=0

Wy multiply elements

-96w^2+6w+(-12w)=0

We get rid of parentheses

-96w^2+6w-12w=0

We add all the numbers together, and all the variables

-96w^2-6w=0

a = -96; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-96)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-96}=\frac{0}{-192}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-96}=\frac{12}{-192}
=-1/16
$