-4+w+17+-2/3w=16

Solution for -4+w+17+-2/3w=16 equation:

-4+w+17+-2/3w=16

We move all terms to the left:

-4+w+17+-2/3w-(16)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


determiningTheFunctionDomain
w-2/3w-4+17-16+=0

We add all the numbers together, and all the variables

w-2/3w=0

We multiply all the terms by the denominator


w*3w-2=0

Wy multiply elements

3w^2-2=0

a = 3; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·3·(-2)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*3}=\frac{0-2\sqrt{6}}{6}
=-\frac{2\sqrt{6}}{6}
=-\frac{\sqrt{6}}{3}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*3}=\frac{0+2\sqrt{6}}{6}
=\frac{2\sqrt{6}}{6}
=\frac{\sqrt{6}}{3}
$