\[\boxed{\text{741.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[x^{2} - (4k + 1)x + 2 \cdot\]
\[\cdot \left( 2k^{2} + k - 3 \right) = 0\]
\[D = (4k + 1)^{2} - 4 \cdot 2 \cdot\]
\[\cdot \left( 2k^{2} + k - 3 \right) = 16k^{2} + 8k +\]
\[+ 1 - 16k^{2} - 8k + 24 =\]
\[= 25\]
\[x_{1,2} = \frac{4k + 1 \pm 5}{2}\]
\[x_{1} = \frac{4k + 1 + 5}{2} =\]
\[= \frac{4k + 6}{2} = 2k + 3\]
\[x_{2} = \frac{4k + 1 - 5}{2} =\]
\[= \frac{4k - 4}{2} = 2k - 2\ \]
\[Ответ:x = 2k + 3;\ \ x = 2k - 2.\]