x\sqrt{x}x - 6x\;\frac{6}{\sqrt{x}}x6 = 1
Multiply through by x\sqrt{x}x
x - 6 = x\sqrt{x}x
x - x\sqrt{x}x = 6
let x\sqrt{x}x = q, then x = q2^22
q2^22 - q - 6 = 0
q2^22 - 3q + 2q - 6 = 0
q(q - 3) + 2(q - 3) = 0
(q - 3)(q + 2) = 0
q = 3 or -2
but x = q2^22, meaning, x = 9 or 4.
