Solve for t

There are two ways that I can think of:

1)  Graphing:  answers  =  1.0897554  and  3.9102446

2)  Quadratic formula:    ((7+(4*(3^(1/2))))^(t^2-5 t+5))+((7-(4*(3^(1/2))))^(t^2-5 t+5))=14

      Notice that, on the left side, you have two equal terms, the equation can be reduced to:

       2*((7-(4*(3^(1/2))))^(t^2-5 t+5))=14

      which becomes:  (7-(4*(3^(1/2)))^(t^2-5 t+5)=7

      Take the log of both sides:  log(7-(4*(3^(1/2)))^(t^2-5 t+5)  =  log(7)

       --->   (t^2-5 t+5) * log(7-(4*(3^(1/2)))  =  log(7)

       --->  (t^2-5 t+5)  =  log(7) / log(7-(4*(3^(1/2)))

       --->  t^2-5 t+5  =  0.9774385152

       --->  t^2-5 t+ (5 - 0.9774385152)  =  0

       --->  a = 1,  b = -5,  c = (5 - 0.9774385152)

       Placing these values into the quadratic formula gives the same results.

Very nice, geno.......I was gonna' look at this one.....but when I saw all those parentheses.....uh, no.......now, after seeing your answer, I realize it's not as bad as all that.....