Find the number of real solutions of $x^7 + 2x^5 + 3x^3 + 4x = 2018$?
What is the general approach to solving this kind of questions? I am interested in the thought process.
Few of my thoughts after seeing this question: since $x$ has all odd powers so, it can not have any negative solution. 2018 is semiprime; not much progress here. We can sketch the curve but graphing a seven order polynomial is difficult.