Help with some geometry problems!

Hello people, it’s my first thread and I hope not the last one.
I installed Blender like an hour ago, and I noticed before this a geometry problem on an object I created in 3ds Max because I made a pro-boolean.
The thing is like this:

In 3ds Max I could fix this by addind some vertices, deleting that highlighted vertex and then welding (or something like that, I’m not a pro neither on 3ds Max).
How could I fix this on Blender?

Pro-Booleans = expect crap result. for clean meshes just model them and don’t rely on ‘automatic’ solutions that require manual cleanup

Select an vertex/edge and X / dissolve to remove it
Select 2 adjacent triangles and press F to make a quad
Alt+M merges selected vertices
K = knife tool
Ctrl+V = vertex tools
Ctrl+E = edge tools
Ctrl+F = face tools

Use the tools in whatever combination to give the result you require

Richard forgot [CTRL R] to add loop cuts. That can help too.