Решите уравнение: x^2-x(корень из (7)-2)-2*корень из 7=0.

\[x² - x\left( \sqrt{7} - 2 \right) - 2\sqrt{7} = 0\]

\[D = \left( \sqrt{7} - 2 \right)^{2} - 4 \cdot 1 \cdot \left( - 2\sqrt{7} \right) =\]

\[= 7 - 4\sqrt{7} + 4 + 8\sqrt{7} =\]

\[= 11 + 4\sqrt{7}\]

\[\sqrt{11 + 4\sqrt{7}} = \sqrt{7 + 4\sqrt{7} + 4} =\]

\[= \sqrt{\left( \sqrt{7} + 2 \right)^{2}} = \sqrt{7} + 2.\]

\[x_{1} = \frac{\sqrt{7} - 2 + \sqrt{7} + 2}{2} =\]

\[= \frac{2\sqrt{7}}{2} = \sqrt{7};\ \ \ \]

\[x_{2} = \frac{\sqrt{7} - 2 - \sqrt{7} - 2}{2} =\]

\[= - \frac{4}{2} = - 2.\]

\[Ответ:\ x = \sqrt{7};\ \ x = - 2.\]