$ \eqalign{ & 2 + \frac{1} {x} = x \cr & 2x + 1 = x^2 \cr & x^2 - 2x - 1 = 0 \cr & (x - 1)^2 - 2 = 0 \cr & (x - 1)^2 = 2 \cr & x - 1 = \pm \sqrt 2 \cr & x = 1 \pm \sqrt 2 \cr} $
