[tex] \frac{1}{x} = \frac{x}{5x + 6} \\ {x}^{2} = 5x + 6 \\ {x}^{2} - 5x - 6 = 0[/tex]

По теореме Виета:

[tex]{x}^{2} + bx + c = 0 \\ x _{1} + x_{2} = - b \\ x _{1} x_{2} = c[/tex]

[tex] {x}^{2} - 5x - 6 = 0 \\ x_{1} + x_{2} = 5\\ x_{1} x_{2} = - 6\\ x_{1} = - 1\\ x_{2} = 6[/tex]