Indicipline girl,
It seems to me the equation you give is correct in principle, but the constant (which you give as 89.1) is wrong.
pkkapkka gives the exact equation in terms of Mach number.
Assume that that ram rise = TAT - SAT and that Mach number = TAS / sqrt(gama*R*SAT)
Then the constant in your equation should be sqrt(5*gama*R).
gama for air is 1.4
In SI units, R for air is 287.05
This gives the constant as 44.826 m/s
Converting to knots gives 87.13
The ADC cannot use the reverse of your equation to compute SAT because it cannot calculate TAS untill it has first calculated SAT. The ADC uses the Mach number equation to compute SAT because it can compute Mach number from pitot - static pressures independantly of temperature.