Надо уединить корень.
5\\\\Otvet:\; x=\frac{11+\sqrt{17}}{2}" alt="\sqrt{x-1}=x-5,\quad ODZ:\; \left \{ {{x-1 \geq 0} \atop {x-5 \geq 0}} \right. \; \to \; x \geq 5\\\\x-1=(x-5)^2\\\\x-1=x^2-10x+25\\\\x^2-11x+26=0\\\\D=121-104=17\\\\x_1=\frac{11-\sqrt{17}}{2}\approx 3,44<5,\\\\x_2=\frac{11+\sqrt{17}}{2}\approx 7,56>5\\\\Otvet:\; x=\frac{11+\sqrt{17}}{2}" align="absmiddle" class="latex-formula">