Let the coefficients of the middle terms in the expansion of (1/(√ 6)+β x)^4,(1-3 β x)^2 and (1-(β)/2 x)^6, β>0, respectively form the first three…

Let the coefficients of the middle terms in the expansion of $\displaystyle \left(\frac{1}{\sqrt{6}}+\beta x\right)^4,(1-3 \beta x)^2$ and $\displaystyle \left(1-\frac{\beta}{2} x\right)^6, \beta>0$, respectively form the first three terms of an A.P. If d is the common difference of this A.P., then $\displaystyle 50-\frac{2 d}{\beta^2}$ is equal to \_\_\_\_.