Are you SURE you have entered the equation correctly? Is a negative sign missing somewhere? Is it perhaps (0.5^.8t) ? SOmeone might be able to sove this , but it is long!
If the domain of t lies between -infinity and +infinity, the range of the right hand side lies between 0 and 1. Hence there is no value of t that allows the right hand side to equal 95350.
+36916 
