I presume what relative min means is local min. As the function goes to -inf when x goes to +- inf, there is no absolute min. However if you plot it you'll probably see it goes up, then down, then up again, then down so it's a sort of M shape. The bottom of the middle bit is your local (relative) min.
The only way to do this without using calculus is to work out roughly where the min is by plotting it or whatever, and then seeing what happens either side of where you think the minimum is (you'll probably find there's a x^2 term in there which will be zero and therefore either side of it it goes + so making the function go uphill. Or something.