Verified answer

[tex]5 - \frac{8}{ {x}^{2} } = \frac{18}{x} \\ 5 - \frac{8}{ {x}^{2} } - \frac{18}{x} = 0 \\ \frac{5 {x}^{2} - 18x - 8 }{ {x}^{2} } = 0 \\ {5x}^{2} - 18x - 8 = 0 \\ d = ( - 18) {}^{2} - 4 \times 5 \times ( - 8) = \\ 324 + 160 = 484 \\ x_{1} = \frac{18 + 22}{2 \times 5} = \frac{40}{10} = 4 \\ x _{2} = \frac{18 - 22}{2 \times 5} = - \frac{4}{10} = - 0.4 \\ x_{1} \times x _{2} = 4 \times ( - 0.4) = - 1.6[/tex]