Descartes' Rule of Signs says there is one real positive root. The FTA says there are 7 roots, so the rest are complex.

You can tell from the graph 'whereabouts' it lies. Therefore, you should be able to find n and n+1 from that.

Also, try Newton's method with an initial guess of 1. That'll give it to you and converges rather quickly.

The Intermediate Value Theorem may also be an course to take.

For that, try x=1 and x=2. Respectively, they give you -1 and 127. So, you know it's in between 1 and 2.

If you try it at x=1.1 you get 0.0487171. So, you see it's between 1 and 1.1. Keep whittling.

More accurately, the root is at