I have the following polynomial $$f(x,Q)=0.064x^6+0.96x^4+4.8x^2-(13.824Q)x+8=0$$ where the variable $Q$ is in the range $]1,2\pi]$. This polynomial is obtained from an equation that describes a nozzle. From the theory I know there are certainly two positive real roots: I have done the check for different values of $Q$ and Wolfram confirms it.
I need the formula to get the two real positive solutions by only changing the value of $Q$: then I have to implement this formula in MATLAB. For what I have written above I think the sextic has a solvable Galois group so can be exactly expressed in terms of radicals.
I am an aerospace engineer and to be honest I don't know where to start with Galois theory.