The Henderson-Hasselbach equation gives approximately 5% concentration error for H_{3}O^{+} with a ratio c_acid/K_acid of about 500 and more (which is equivalent to the error of about 0.02 pH units). In this example, this ratio is equal to 1. Therefore, the author uses a different, but sufficient, simplification - it takes into account the dissociation of the acid, and ignore the autoprotolysis of water and the effect of ionic strength.

This simplification leads to a quadratic equation.