\[x^{2} - 4bx + 3b + 1 = 0\]
\[D = 16b^{2} - 12b - 4 > 0\ \ \ \ |\ :4\]
\[4b^{2} - 3b - 1 = 0\]
\[D = 9 + 16 = 25\]
\[b_{1} = \frac{3 + 5}{8} = 1\]
\[b_{2} = \frac{3 - 5}{8} = - \frac{1}{4}\]
\[Ответ:( - \infty;\ - 0,25) \cup (1; + \infty).\]