DISCLAIMER: I apologize in advance if this question is naive. Every suggestion on how to approach the following problem will be very much appreciated.
I'm interested in the root of the following function:
$f(x)= [(2x-x^2)\cdot (2x-x^2)] -x$
If I use some software to draw this function, I can see a root around x=0.38, let's call it R.
my questions are: A) How can I calculate R? I don't know how to handle equations of 4th order B) I'm very interested in knowing if R is irrational.
Thank you in advance