Answer
$$\frac{{dy}}{{dx}} = - 20 - \frac{{50}}{3}x$$
Work Step by Step
$$\eqalign{
& \frac{{6 + 5x}}{{2 - 3y}} = \frac{1}{{5x}} \cr
& {\text{cross product}} \cr
& 5x\left( {6 + 5x} \right) = 2 - 3y \cr
& 60x + 25{x^2} = 2 - 3y \cr
& {\text{take the derivative on both sides with respect to }}x \cr
& \frac{d}{{dx}}\left( {60x + 25{x^2}} \right) = \frac{d}{{dx}}\left( {2 - 3y} \right) \cr
& {\text{solve the derivatives }} \cr
& 60 + 50x = 0 - 3\frac{{dy}}{{dx}} \cr
& {\text{solve for }}\frac{{dy}}{{dx}} \cr
& 60 + 50x = 0 - 3\frac{{dy}}{{dx}} \cr
& \frac{{dy}}{{dx}} = \frac{{60 + 50x}}{{ - 3}} \cr
& \frac{{dy}}{{dx}} = - 20 - \frac{{50}}{3}x \cr} $$
