\[x^{4} - 20x^{2} - 69 = 0\]
\[Пусть\ x^{2} = y \geq 0:\ \]
\[y^{2} - 20y - 69 = 0\]
\[D = 100 + 69 = 169\]
\[y_{1} = 10 + 13 = 23;\ \ \ \]
\[y_{2} = 10 - 13 = - 3\ (не\ подходит).\]
\[x^{2} = 23\]
\[x = \pm \sqrt{23}.\]
\[Ответ:x = \pm \sqrt{23}\text{.\ }\]