Big O proofing, need explanation on how to get the answer.

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I have spent the whole day trying to understand Big O but I'm still confused. Hopefully someone can enlighten me. I have an example: $100+5∈(^2)$ [so i know $100n+5$ is Big O of $n^2$] [the image is the steps in solving the equation]1 So my question is: Why $n_0 = 15$ and $c =7$? How do I get it?