If I were to get 3 web servers in different locations of the united states and load balanced them how would that work with a single Linode managed database? Would it mess up reads/writes. Or would it work flawlessly?
With additional information about how you intend to set this up, someone from our Community may have more specific guidance to offer. For now, I wanted to try to provide some information to help you figure this out.
We've had some similar questions to this one in the past, though they aren't exactly the same. I think they could be helpful though.
First, this post about syncing managed databases across regions points out that the managed clusters themselves can't be connected across regions. That said, you should be able to access the cluster from servers in other regions using the public network host. You'd only be able to connect to the private host from the same data center.
Since you can connect to the cluster from other regions, you may be able to then use HAProxy or NGINX to configure loadbalancing. While I didn't test this, I wasn't able to see any obvious blockers with either of those working with Managed Databases.
That post first offers a solution that I have a feeling would end up being the best option for you here, which involves creating a self-managed cluster instead:
We have a few options for deploying clusters as Marketplace Apps for MariaDB, PostgreSQL, and Redis if you decide to go that route.