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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

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

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

We get rid of parentheses

1/2w-2/3w-3/4=0

We calculate fractions


(-54w^2)/96w^2+48w/96w^2+(-64w)/96w^2=0

We multiply all the terms by the denominator


(-54w^2)+48w+(-64w)=0

We get rid of parentheses

-54w^2+48w-64w=0

We add all the numbers together, and all the variables

-54w^2-16w=0

a = -54; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-54)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-54}=\frac{0}{-108}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-54}=\frac{32}{-108}
=-8/27
$