help!

Call this "x" : $\cfrac{9}{9 + \cfrac{9}{9 + \cfrac{9}{9 + \dotsb}}}$

Which simplifies to: $\frac{9}{9+x}$

From this, we can set up the equations:
$x=\frac{9}{9+x}$

$x^2+9x=9$

$x^2+9x-9=0$---> This quadratic equation had 2 solutions, one positive and one negative, for obvious reasons we can rule out the negative solution. This means that the positive solution is our answer:

$x=\frac{-9+3\sqrt{13}}{2}$

I appreciate your time!


*Note: I'm not 100% sure about my answer. If anyone sees anything wrong with my thinking process, make sure to point it out!