Hitting a roadblock while solving a logarithmic equation $$x^{ 5-\log _{ 3 }{ x }  }=9x^2$$
Steps I took:
$$\log _{ 3 }{ x^{ 5-\log _{ 3 }{ x }  } } =\log _{ 3 }{ 9x^{ 2 } } $$
$$(5-\log _{ 3 }{ x } )(\log _{ 3 }{ x) } =\log _{ 3 }{ 9x^{ 2 } } $$
$$5\log _{ 3 }{ x } -(\log _{ 3 }{ x } )^{ 2 }=\log _{ 3 }{ 9x^{ 2 } } $$
$$(\log _{ 3 }{ x } )^{ 2 }-5\log _{ 3 }{ x } =-\log _{ 3 }{ 9x^{ 2 } } $$
I am trying to turn this into a quadratic equation to then solve with substitution, but I can't seem to manipulate the right hand side of this equation in any way that will allow me to do this. 
Hints are much better appreciated than the actual answer.  

Something to try: 
Convert your right side to
$$-\log _{ 3 }{ 9x^{ 2 } }=-\log _{ 3 }{( 3x)^{ 2 } }=-2\log_{3}{(3x)}$$
Then you convert your left-side terms to $$\log_{3}{(3x)}$$ instead of $$\log_{3}{(x)}$$  
See where that takes you.
