-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


We add all the numbers together, and all the variables

w+2/3w-3=0

We multiply all the terms by the denominator


w*3w-3*3w+2=0

Wy multiply elements

3w^2-9w+2=0

a = 3; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·3·2
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{57}}{2*3}=\frac{9-\sqrt{57}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*3}=\frac{9+\sqrt{57}}{6}
$