What is the maximum number of triangles we can draw in a planar graph using at most 30 nodes and 50 edges I'm trying to solve this problem because I need to implement it into my program for calculating some values related to this.

Namely, I need to find what is the maximum number of triangles we can draw if we can use only up to 30 nodes and up to 50 edges. The triangles can share point, points or sides.

I started thinking if we can put one point in the center and then we put all the other points around it and then connect with the point in the center, but it looks like this wont be the maximum number.
I got 50 edges 19 nodes 32 triangles.
Take the complete graph on 10 nodes. It needs ${10 \choose 2}=45$ edges. You get ${10 \choose 3}=120$ triangles. And you have 5 more edges.