2. What is the sum of all the solutions of the equation $6 x=\frac{150}{x}$ ?
A 0
B 5
C 6
D 25
E 156
SOLUTION
We have,
$$
\begin{aligned}
6 x=\frac{150}{x} & \Leftrightarrow 6 x^{2}=150 \\
& \Leftrightarrow x^{2}=25 \\
& \Leftrightarrow x=-5 \text { or } x=5 .
\end{aligned}
$$

Therefore the equation has the two solutions -5 and 5 . It follows that the sum of all the solutions of the equation is $-5+5=0$.

Note that here the symbol $\Leftrightarrow$ stands for if, and only if.