[tex] \frac{29}{10} = x + \frac{1}{x} \\ 29 = 10x + \frac{10}{x} \\ 10x - 29 + \frac{10}{x} = 0 \\ 10 {x}^{2} - 29x + 10 = 0 \\ \frac{29 + \sqrt{841 - 400} }{20} = x \\ \frac{29 + \sqrt{441} }{20} = x \\ \frac{29 + 21}{20} = \frac{50}{20} = 2 \frac{1}{2} = x \\ or \\ \frac{29 - \sqrt{841 - 400} }{20} = x \\ \frac{29 - \sqrt{441} }{20} = x \\ \frac{29 - 21}{20} = \frac{8}{20} = \frac{2}{5} = x[/tex]
