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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

w-2/3w-4=0

We multiply all the terms by the denominator


w*3w-4*3w-2=0

Wy multiply elements

3w^2-12w-2=0

a = 3; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·3·(-2)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{42}}{2*3}=\frac{12-2\sqrt{42}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{42}}{2*3}=\frac{12+2\sqrt{42}}{6}
$