Chapter 8 - Section 8.2 - Solving Quadratic Equations by the Quadratic Formula - Exercise Set - Page 494: 69

$x=15$

Multiplying both sides of the given equation, $ \dfrac{1}{x}+\dfrac{2}{5}=\dfrac{7}{x} ,$ by the $LCD= 5x $, then, \begin{array}{l}\require{cancel} 5x\left( \dfrac{1}{x}+\dfrac{2}{5} \right)=\left( \dfrac{7}{x} \right)(5x) \\\\ 5(1)+x(2)=7(5) \\\\ 5+2x=35 \\\\ 2x=35-5 \\\\ 2x=30 \\\\ x=\dfrac{30}{2} \\\\ x=15 .\end{array}