Verified answer

[tex] \frac{2}{ {x}^{2} } + \frac{8}{x} = 2 \\ \frac{2}{ {x}^{2} } + \frac{8}{x} - 2 = 0 \\ \frac{ - 2 {x}^{2} + 8x + 2 }{ {x}^{2} } = 0 \\ - 2 {x}^{2} + 8x + 2 = 0 \\ {x}^{2} - 4x - 1 = 0 \\ d = ( - 4) {}^{2} - 4 \times ( -1 ) = 16 + 4 = 20 \\ ( \sqrt{d} = 2 \sqrt{5} ) \\ x _{1} = \frac{4 + 2\sqrt{5} }{2} = \frac{2(2 + \sqrt{5} )}{2} = 2 + \sqrt{5} \\ x_{2} = \frac{4 - 2 \sqrt{5} }{2 } = \frac{2(2 - \sqrt{5}) }{2} = 2 - \sqrt{5} [/tex]