3/4w+1/6+1/2w=3/4

Solution for 3/4w+1/6+1/2w=3/4 equation:

3/4w+1/6+1/2w=3/4

We move all terms to the left:

3/4w+1/6+1/2w-(3/4)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

3/4w+1/2w+1/6-(+3/4)=0

We get rid of parentheses

3/4w+1/2w+1/6-3/4=0

We calculate fractions


64w^2/1152w^2+216w/1152w^2+576w/1152w^2+(-216w)/1152w^2=0

We multiply all the terms by the denominator


64w^2+216w+576w+(-216w)=0

We add all the numbers together, and all the variables

64w^2+792w+(-216w)=0

We get rid of parentheses

64w^2+792w-216w=0

We add all the numbers together, and all the variables

64w^2+576w=0

a = 64; b = 576; c = 0;
Δ = b2-4ac
Δ = 5762-4·64·0
Δ = 331776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{331776}=576$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-576}{2*64}=\frac{-1152}{128}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+576}{2*64}=\frac{0}{128}
=0
$