Решить уравнение √5х-6-√х-2=2

$\displaystyle\mathtt{\left\{{{(\sqrt{5x-6})^2=(\sqrt{x-2}+2)^2}\atop{5x-6\geq0~and~x-2\geq0}}\right\left\{{{5x-6=x-2+4\sqrt{x-2}+4}\atop{x\geq\frac{6}{5}~and~x\geq2}}\right}\\\\\mathtt{\left\{{{4x-8=4\sqrt{x-2}}\atop{x\geq2}}\right\left\{{{x-2=\sqrt{x-2}}\atop{x\geq2}}\right\left\{{{\left[\begin{array}{ccc}\mathtt{x-2=0}\\\mathtt{x-2=1}\end{array}\right}\atop{x\geq2}}\right\left\{{{\left[\begin{array}{ccc}\mathtt{x=2}\\\mathtt{x=3}\end{array}\right}\atop{x\geq2}}\right}$

ответ: $\mathtt{x=2;~3}$