Question

Find the positive number which is 5 more than 14 times its reciprocal.

Answer 1

Let the number be x.
Given,
$x = 14 \times \frac{1}{x} + 5 \\ x = \frac{14 + 5x}{x} \\ {x}^{2} - 5x - 14 = 0 \\ (x - 7)(x + 2) = 0 \\ x = 7 \: \: or \: \: - 2$

Since the number is positive, x = 7