You Can't Get An Equation Shorter Than This.

Algebra Level 5

If the sum of all real solutions of the equation : {x}x=2014x\left\{x\right\}\left\lfloor x\right\rfloor =2014 x can be written as ab\frac{-a}{b} where a,ba,b are coprime positive integers, find a+ba+b.


Details and assumption :

\left\lfloor \cdot\right\rfloor is the floor function (the greatest integer function) and {x}=xx\{x\}=x-\left\lfloor x\right\rfloor .

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