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Construction of schedules for the inequality decision

Good afternoon.

I need to solve difficult enough inequality

The given inequality breaks into 2 cases

Equality  b^2=4ac sets some cone, and equalities

set Two-Sheeted Hyperboloidand and One-Sheeted Hyperboloid accordingly. Points between the given hyperboloids also will be decisions of the set inequality.
Question: how in Mathematica to draw drawing to the decision of this problem? This point in question is very important for me.

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