Помогите угадать корень уравненияx - 1/x = 6 6/7

Решите задачу:

$x- \frac{1}{x} =6 \frac{6}{7} \\ x- \frac{1}{x} = \frac{48}{7}/*7x \neq 0 \\ 7x \neq 0 \\ x \neq 0 \\ 7 x^{2} - \frac{7x}{x} = \frac{48*7x}{7} \\ 7 x^{2} -7=48x \\ 7 x^{2} -48x-7=0 \\ D=2304+4*7*7=2304+196=2500 \\ \sqrt{D} =50 \\ x_{1} = \frac{48+50}{14} = \frac{98}{14} =7 \\ x_{2} = \frac{48-50}{14} = \frac{-2}{14} =- \frac{1}{7}$