To perform division in complex numbers, we multiply both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of $ 1+2i $ is $ 1-2i $. Multiplying: \begin{align*} \frac{-3+4i}{1+2i}&=\frac{(-3+4i)(1-2i)}{(1+2i)(1-2i)}\\ &=\frac{-3+4i+6i-8i^2}{1+2i-2i-4i^2}\\ &=\frac{5+10i}{5}\\ &=\boxed{1+2i} \end{align*}