3.77: Binomial expansion: independent term and coefficient of $x^{6}$

In the expansion of $\left(ax + \dfrac{b}{x^{2}}\right)^{9}$, where $a$ and $b$ are constants with $a > 0$, the term independent of $x$ is $-145\,152$ and the coefficient of $x^{6}$ is $-6912$. Show that $a^{2}b = -12$ and find the value of $a$ and the value of $b$.