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If the roots of $$2016x^2 + bx + c = 0$$ are $$\frac{5}{63}$$, $$-\frac{7}{32}$$ then $$b + 6c$$ is equal to
Sum of roots $$= \frac{5}{63} - \frac{7}{32} = \frac{160 - 441}{2016} = -\frac{281}{2016} = -\frac{b}{2016}$$, so $$b = 281$$. Product of roots $$= -\frac{35}{2016} = \frac{c}{2016}$$, so $$c = -35$$. Hence $$b + 6c = 281 - 210 = 71$$.
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