If a tile pattern can be described by the equation $y=\left(x-1\right)\left(x+1\right)+x+2$, where $x$ represents the figure number and $y$ represents the number of tiles, find each of the following.  

1. The number of tiles in Figure $307$.

   Hint 1(a):

   Substitute 307 into the equation for $x$.

   $y=\left(307-1\right)\left(307+1\right)+307+2$

   Hint 2(a):

   Solve for $y$.

   Answer (a):

   $y = 94{,}557$

2. The number of the figure that contains $169{,}333$ tiles.

   Hint 1(b):

   Set $y = 169{,}333$.

   $169,333=\left(x-1\right)\left(x+1\right)+x+2$

   Hint 2(b):

   Solve for $x$.