A word problem is given which I've answered correctly, but a second question doesn't add up. The problem is:

A North-South highway intersects an East-West highway at a point P. An automobile crosses P at 10:00 AM, traveling east at a constant rate of 20 mph. At that same instant another automobile is two miles north of P, traveling south at 50 mph. Find a formula which expresses the distance d between the automobiles at time t (hours) after 10:00 AM. At what time will the automobiles be 104 miles apart?

My answer, which the book confirms, is

$\displaystyle d = \sqrt{2900t^2 - 100t + 4}$

To answer the second question, I started with

$\displaystyle 104 = \sqrt{2900t^2 - 100t + 4}$

$\displaystyle \Rightarrow 10816 = 2900t^2 -100t + 4$

$\displaystyle \Rightarrow 2704 = 725t^2 - 25t + 1$

$\displaystyle \Rightarrow 725t^2 - 25t - 2703 = 0$

Using the Quadratic Formula, I get

$\displaystyle \frac {25 \pm \sqrt {625 + 7838700}} {1450}$

which I can only reduce to

$\displaystyle \frac {5 \pm \sqrt {313573}} {290}$

But the answer given in the book is:

$\displaystyle \frac {1 + \sqrt 30} {29}$

So how do I get there? Did I make a mistake along the way?