x=1 y= x=1151 y=120 x=2649601 y=276240 etc.

Each successive solution is about 2300 times the previous solution; they are every 8th partial fraction (x=numerator, y=denominator) of the continued fraction for sqrt(92) =

[9, 1,1,2,4,2,1,1,18, 1,1,2,4,2,1,1,18, 1,1,2,4,2,1,1,18, ...?

Once you have the smallest positive solution (x1,y1) you don't need to "search" for the rest. You can obtain the nth positive solution (xn,yn) by the formula

(x1 + y1 sqrt(92))^n = xn + yn sqrt(92).

See Niven & Zuckerman's An Introduction to the Theory of Numbers. Look in the index under Pell's equation.