Solve for $x$, where $x>0$ and $5x^2+9x-18=0$. Express your answer as a simplified common fraction.
$5x^2+9x-18$ can be written as $(5x-6)(x+3)$. Because $x$ must be positive, the only factor that can be considered is $(5x-6)$. Therefore: \begin{align*}
5x-6&=0\\
5x&=6\\
x&=\boxed{\frac{6}{5}}
\end{align*}