(x + 2/x)^2 = 6
(x + 2/x) = + - sqrt(6)
x^2 + 2 = + - (sqrt(6))*x
x^2 + - (sqrt(6))x + 2 = 0

x = ( + - sqrt(6) + - sqrt(6 MINUS 4*1*2) ) / 2

x = (+ - sqrt(6) + - sqrt(-2)) / 2

x is a complex number, however that doesn't mean the problem doesn't have an answer.