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Look at this picture:

Point ##B## is at the half the distance between ##q## and ##2q##. What I am trying to prove/disprove

That there might be actually a point (##A##) near of charge ##2q## that might have an electric field stronger than the electric field at point ##B##

It seems rational that this could happen

Assume that the distance is ##r##

By equaling the magnitude of the electric field at both points, We will have this equation

$$ \frac{2}{x^2} = \frac{12}{r^2} +\frac{1}{(r+x)^2} $$

The math becomes difficult here, Is there is a way to perhaps simplify the math here? Should I put some random value of r?

Useful notes: x should be really small

Another question here, does the field have the maximum magnitude at the r/2? Is there is a way to prove that too?