50p^2-2600p-22500=0 what is the answer

You could make this problem simpler by dividing all 4 terms by 50:

p^2 - 52p - 450 = 0

To solve this we could use any of the following:

graphing
completing the square
quadratic formula
factoring

I'll use the quadratic formula.  Here, a=1, b= -52 and c = -450.

                -(-52) plus or minus sqrt( [-52]^2 - 4(1)(-450)
Then x =
                                                2
                                      52 plus or minus sqrt(4504)
This simplifies to   x =
                                                          2

Unfortunately, the answers are not "nice."
                                   52 plus or minus 67.11
                          x =
                                                 2

Can you simplify these results further?

If I try completing the square, I obtain from p^2 - 52p - 450 the following:

p^2 - 52p + (-26)^2  - (-26)^2 - 450 = 0  =>  (p-26)^2 - 676 - 450 = 0.

This results in (p-26)^2 - 1126 = 0, or 

(p-26)^2 = 1126

Then p-26 = plus or minus 33.56, or

p = 26 plus or minus 33.56.

Igot the answer of 15.8 years.

B12/23 is your answer