Question: solve() mystery

I have been severely mystified by the following:
                                                                                                                      
I have an implicit expression for the variable v[a1]:                                              

>expr:=-1.923342953*10^7+1.600000000*10^(-10)*sqrt(-6.836648013*10^9*v[a1]^2+1.445018797*10^34) = 0.2000000000e-1;

>RealDomain[solve](expr,v[a1]);                             this gets no output - apparently no real solutions, but then...

>eval(expr,v[a1]=1.959842954*10^7);                     this results in 0.02 = 0.02000000000 - so there is  a                                               

                                                                             real solution?

What's going on here? O_O I suspect it has something to do with round-off errors