If the constant term in the binomial expansion of ((x^(5/2))/2-4/x^l)^9 is -84 and the coefficient of x^-3 l is 2^α β, where β<0 is an odd number,…

If the constant term in the binomial expansion of $\displaystyle \left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^l}\right)^9$ is -$\displaystyle 84$ and the coefficient of $\displaystyle x^{-3 l}$ is $\displaystyle 2^\alpha \beta$, where $\displaystyle \beta<0$ is an odd number, then $\displaystyle |\alpha l-\beta|$ is equal to $\displaystyle \_\_\_\_$.