factor x^(n+6) +x^(n+2) + X^n

and solve x^2-5x+2/3=0

x^(n+6) +x^(n+2) + X^n

I see a common factor of x^n

= x^n( x^6 + x^2 + 1)

solving x^2 - 5x + 2/3 = 0
3x^2 - 15x + 2 = 0
x = (15 ± √201)/6