$$\left. \begin{array} { l } { ( 2 k + 1 ) x ^ { 2 } - ( 7 k + 3 ) x + k + 2 = 0 } \\ { \text { a r e r e c i p r o e a l t o e \right.$$
$\left\{\begin{matrix}x=\frac{\sqrt{41k^{2}+22k+1}+7k+3}{2\left(2k+1\right)}\text{; }x=\frac{-\sqrt{41k^{2}+22k+1}+7k+3}{2\left(2k+1\right)}\text{, }&k\neq -\frac{1}{2}\\x=-3\text{, }&k=-\frac{1}{2}\end{matrix}\right.$
$\left\{\begin{matrix}x=\frac{\sqrt{41k^{2}+22k+1}+7k+3}{2\left(2k+1\right)}\text{; }x=\frac{-\sqrt{41k^{2}+22k+1}+7k+3}{2\left(2k+1\right)}\text{, }&\left(k\neq -\frac{1}{2}\text{ and }k\leq \frac{-4\sqrt{5}-11}{41}\right)\text{ or }k\geq \frac{4\sqrt{5}-11}{41}\\x=-3\text{, }&k=-\frac{1}{2}\end{matrix}\right.$
