How to get the conditions required to analyze the result?

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I'm struggling to understand the method followed in the following analysis. Can someone please explain, how the author got the values of $Δ_1$ and $K_1$ and justify its analysis.

I have tried to isolate "$Δ$" and "$K$" by setting Equation (B8) equal to zero. But I have failed to get the similar conditions.

P.S: I'm new to mathematical modelling, so I really need to understand whats going on here. Thanks.