2/3w+1/6+1/2w=34

Solution for 2/3w+1/6+1/2w=34 equation:

2/3w+1/6+1/2w=34

We move all terms to the left:

2/3w+1/6+1/2w-(34)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


determiningTheFunctionDomain
2/3w+1/2w-34+1/6=0

We calculate fractions


12w^2/216w^2+144w/216w^2+108w/216w^2-34=0

We multiply all the terms by the denominator


12w^2+144w+108w-34*216w^2=0

We add all the numbers together, and all the variables

12w^2+252w-34*216w^2=0

Wy multiply elements

12w^2-7344w^2+252w=0

We add all the numbers together, and all the variables

-7332w^2+252w=0

a = -7332; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-7332)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-7332}=\frac{-504}{-14664}
=21/611
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-7332}=\frac{0}{-14664}
=0
$