$$\eqalign{
& P = x - 2\sqrt {2x - 3} \cr
& DK:\,\,2x - 3 \ge 0 \Leftrightarrow x \ge {3 \over 2} \cr
& f\left( x \right) = x - 2\sqrt {2x - 3} \cr
& f'\left( x \right) = 1 - {{2.2} \over {2\sqrt {2x - 3} }} = 1 - {2 \over {\sqrt {2x - 3} }} = 0 \cr
& \Leftrightarrow \sqrt {2x - 3} = 2 \Leftrightarrow 2x - 3 = 4 \Leftrightarrow x = {7 \over 2}\,\,\left( {tm} \right) \cr
& Lap\,\,\,BBT \cr
& \Rightarrow \min f\left( x \right) = \left( {{7 \over 2}} \right) = {7 \over 2} - 2\sqrt {2.{7 \over 2} - 3} = - {1 \over 2} \cr} $$
