In "Cycle Compute Divece" appears "none". It's as if I did not have a video card. I have a board [AMD / ATI] Cape Verde PRO [Radeon HD 7750/8740 / R7 250E] It is listed as having Opencl support. This happens with both Linux (Ubuntu) and Windos (Windows 10). Is there a solution?
Your GPU is GCN 1st gen. That's why it's not supported.
Cegaton pointed out in a comment Can't use Radeon GPU to render in cycles (R9 270)
Which is where I figured that out from this list here https://en.wikipedia.org/wiki/List_of_AMD_graphics_processing_units
EDIT: Originally I claimed and cited that Nvidia's Cuda core programming has higher support and faster speeds. However, Cegaton pointed out in the comments that as of Blender Version 2.79 OpenCL has made significant improvements. While OpenCL still is undergoing active development it appears to beat NVidia in the benchmarks, at least in tests comparing a midrange ~$200 graphics cards