x^3 -5x-6=0 can you please tell me how to solve this algebraically? I tried using grouping method x(x^2-5)-6=0, I'm not sure what to do next.
for higher-degree polynomials, try some synthetic division to try and find rational roots. In this case, there are none, so you're stuck with graphical or numeric methods.
A check on the graph will show that there is a single real root, near x = 2.7, but that's about it. You can do a long division, and end up with a quadratic, which you can then tackle using the usual formula.