ok I found the solution myself:
In[12]:= FindMaximum[{x - 2 x^2 && x > 0}, x,
WorkingPrecision -> 8]
Out[12]= {0.12500000, {x -> 0.24995000}}
(that is && insted of ,)
However still I am wondering what made the difference and why with Maximize the "," works and not the "&&"
In[13]:= Maximize[{x - 2 x^2 && x > 0}, x, WorkingPrecision -> 8]
Out[13]= Maximize[{x - 2 x^2 && x > 0}, x, WorkingPrecision -> 8]
In[6]:= Maximize[{x - 2 x^2, x > 0}, x, WorkingPrecision -> 8]
Out[6]= {1/8, {x -> 1/4}}
