A real number $x$ satisfies the equation $\frac{1}{x}+\frac{x}{80}=\frac{7}{30}$. What are the possible values of $x$ ?
Multiplying through by $240 x$, the equation becomes $240+3 x^{2}=56 x$.

This can be rearranged to $3 x^{2}-56 x+240=0$ which factors as $(3 x-20)(x-12)=0$.

Therefore, the possible values of $x$ are $x=12$ and $x=\frac{20}{3}$. Note that these values could also be obtained using the quadratic formula.

One can check that $x=12$ and $x=\frac{20}{3}$ indeed satisfy the equation.

ANSWER: $12, \frac{20}{3}$

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