\[\left( x^{2} + x \right)^{2} - 5 \cdot \left( x^{2} + x \right) + 6 = 0\]
\[Пусть\ a = x^{2} + x:\]
\[a^{2} - 5a + 6 = 0\]
\[a_{1} + a_{2} = 5;\ \ \ \ a_{1} \cdot a_{2} = 6\]
\[a_{1} = 3;\ \ \ a_{2} = 2.\]
\[Подставим:\]
\[1)\ x^{2} + x = 3\]
\[x^{2} + x - 3 = 0\]
\[D = 1 + 12 = 13\]
\[x_{1,2} = \frac{1 \pm \sqrt{13}}{2}.\]
\[2)\ x^{2} + x = 2\]
\[x^{2} + x - 2 = 0\]
\[x_{1} + x_{2} = - 1;\ \ \ x_{1} \cdot x_{2} = - 2\]
\[x_{1} = - 2;\ \ \ x_{2} = 1.\]
\[Ответ:\ \ x = - 2;\ \ x = 1;\ \ \]
\[x = \frac{1 \pm \sqrt{13}}{2}.\]