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