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 .