3/4w+1/6+1/2w=34

Solution for 3/4w+1/6+1/2w=34 equation:

3/4w+1/6+1/2w=34

We move all terms to the left:

3/4w+1/6+1/2w-(34)=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


determiningTheFunctionDomain
3/4w+1/2w-34+1/6=0

We calculate fractions


16w^2/288w^2+216w/288w^2+144w/288w^2-34=0

We multiply all the terms by the denominator


16w^2+216w+144w-34*288w^2=0

We add all the numbers together, and all the variables

16w^2+360w-34*288w^2=0

Wy multiply elements

16w^2-9792w^2+360w=0

We add all the numbers together, and all the variables

-9776w^2+360w=0

a = -9776; b = 360; c = 0;
Δ = b2-4ac
Δ = 3602-4·(-9776)·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-360}{2*-9776}=\frac{-720}{-19552}
=45/1222
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+360}{2*-9776}=\frac{0}{-19552}
=0
$