Did the original equation have rational coefficients, possibly
If so then you can rescale by substitution of
in the equation so it can be transformed to
Sadly, if this is the case then there are no easy roots to find via easy analytical methods (unless you happen to know the cumbersome general solution for a cubic) so the only approach available would be to use a numerical method such as Newton-Raphson method.
So the bottom line is that this will most likely need a numerical method.
To do this I recommend that you first differentiate to find the maximum and minimum coordinates. From these values you should have a rough idea of where the single real root is. You can then put this first good guess into your Newton-Raphson iteration method to find the root.
Finally, don't forget to work backwards to get back to .