How to solve this equation? The following is an error correcting equation for a sidereal astrophotography tracking mount I'm building and $t$ represents the amount of time before the tracking is off by a quarter of a stepper motor step. I need to solve for $t$, but I've having trouble solving this. I can plot it with a value of $n$ and find an ok approximation, but the problem is that I need it for several values of $n$. Any good ways? $n$ is the integer number of corrections applied thus far. If it can't be solved in a general sense, what's a good way to generate approximate solutions for a few hundred values of $n$, starting at 0? $$-0.25=\frac{\sqrt{2\cdot 150^2-2\cdot 150^2\cdot \cos(t\cdot 0.000072733)} - (t\cdot 0.0109170306+(n\cdot -0.25\cdot 0.005))}{0.005}$$

Here is a table of values of $t$ for integers $0\le n\le 500$, generated using Mathematica's FindRoot.

Here are the first few values:


n= 0: t= 174.7
n= 1: t= 339.8
n= 2: t= 489.7
n= 3: t= 623.7
n= 4: t= 743.3
n= 5: t= 850.4
n= 6: t= 947.2
n= 7: t=1035.4
n= 8: t=1116.4
n= 9: t=1191.3
n= 10: t=1261.0


Here's the rough source code:


Table[{n,
t /. FindRoot[-0.25 == (Sqrt[
2*150^2 -
2*150^2*Cos[
t*0.000072733]] - (t*0.0109170306 + (n*-0.25*.005)))/
0.005, {t, 200 + 150 n}]}, {n, 0, 500}]