Counting equilibria of the harvested logistic equation by the discriminant (Q1678)

rN\\Bigl(1-\\frac{N}{K}\\Bigr)-H=0\\ \\iff\\ \\frac{r}{K}N^{2}-rN+H=0;\\qquad \\Delta=r^{2}-\\frac{4rH}{K}\\ \\Rightarrow\\ \\text{two equilibria if }H<H_{c}=\\frac{rK}{4},\\ \\text{one if }H=H_{c},\\ \\text{none if }H>H_{c}