Question: Shading different areas

I wanna shade/fill different areas in a single graph and provide a legend for the graph. Areas are defined as follows where 0<=x<=1 and 0<=z<=1. 

(label = c1) \quad if 0<x<1/13*(5-2sqrt(3)),0<z<1/2(2x+x^2)+1/2sqrt(4x^3+x^4)

 

(label = c2) \quad if 0<x<1/13*(5-2sqrt(3)),1/2(2x+x^2)+1/2sqrt(4x^3+x^4)<z<2x

 

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