3/4w-12=2/3w

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

3/4w-12=2/3w

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9w/12w^2+(-8w)/12w^2-12=0

We multiply all the terms by the denominator


9w+(-8w)-12*12w^2=0

Wy multiply elements

-144w^2+9w+(-8w)=0

We get rid of parentheses

-144w^2+9w-8w=0

We add all the numbers together, and all the variables

-144w^2+w=0

a = -144; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-144)·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*-144}=\frac{-2}{-288}
=1/144
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-144}=\frac{0}{-288}
=0
$