Hi,

log(base x)(5 + 3x - x^2) = 2

 my solution: 

x^2 = 5 + 3x - x^2

 x^2 + x^2 = 5 + 3x

 2x^2 = 5 + 3x

 2x^2 - 5 - 3x = 0

 2x^2 + 2x - 5x - 5 = 0

 2x(x + 1) - 5(x + 1) = 0

 (2x - 5)(x + 1) = 0    Yes.  Good work!

Following thru to the finish...

  x = 5/4  OR x =      

Note:  and 

Always a good idea to check answers found,when it is possible to do so 

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