Solve the following inequality:

$$
\frac{2+7 x-15 x^{2}}{5-x+6 x^{2}}>0
$$
The roots of the equation $6 x^{2}-x+5=0$ are complex numbers, therefore the denominator is positive for all values of $x$, and thus the sign of the fraction depends solely on the sign of the numerator. The numerator is positive when we substitute values for $x$ that lie between the roots of the equation

$$
-15 x^{2}+7 x+2=0
$$

Since the roots of this equation are $\frac{2}{3}$ and $-\frac{1}{5}$, our inequality is satisfied when

$$
-\frac{1}{5}<x<\frac{2}{3}
$$

(Sándor Pichler, Budapest.)