$\sqrt{a}(\sqrt{a}-2)=\sqrt{a}-1$ (ĐK: $a≥0$)
$↔a-2\sqrt{a}-\sqrt{a}+1=0$
$↔a-3\sqrt{a}+1=0$
$↔a-2.\dfrac{3}{2}.\sqrt{a}+\dfrac{9}{4}-\dfrac{5}{4}=0$
$↔(a-\dfrac{3}{2})²-\dfrac{5}{4}=0$
$↔(a-\dfrac{3+\sqrt5}{2})(a+\dfrac{\sqrt 5-3}{2})=0$
$↔a-\dfrac{3+\sqrt 5}{2}=0\quad or\quad a+\dfrac{\sqrt 5-3}{2}=0$
$↔a=\dfrac{3+\sqrt 5}{2}\quad a=-\dfrac{\sqrt 5-3}{2}$ (tm)