AoPS Wiki:Problem of the Day/June 4, 2011

{x} is defined by the smallest positive decimal such that when subtracted from x, you get an integer, and $0<\{x\}<1$

Find x such that $10*{x}^2+\frac{\lfloor x \rfloor}{\lceil x\rceil}=\frac{9}{10}$

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