Well done to Minhaj, Amrit, Adithya, Sasi, Will, Charlie, Luke and Luke, Eric, Pablo, Julian, Johnny, Peter, Gabriel, and Manolis for their hard work on this problem!

$$x^2-14x+1< 0.$$
Use the quadratic formula to solve this inequality. From the graph of $y =x^2 -14x + 1$ we see that the solution is $7-4\sqrt 3 < x < 7+4\sqrt 3$ or approximately $0.072< x< 13.928.$