Answer
$u=3\pm\sqrt{7}$
Work Step by Step
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solution/s of the given equation, $
u^2-6u+2=0
,$ is/are
\begin{array}{l}\require{cancel}
u=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(1)(2)}}{2(1)}
\\\\
u=\dfrac{6\pm\sqrt{36-8}}{2}
\\\\
u=\dfrac{6\pm\sqrt{28}}{2}
\\\\
u=\dfrac{6\pm\sqrt{4\cdot7}}{2}
\\\\
u=\dfrac{6\pm\sqrt{(2)^2\cdot7}}{2}
\\\\
u=\dfrac{6\pm2\sqrt{7}}{2}
\\\\
u=\dfrac{2(3\pm\sqrt{7})}{2}
\\\\
u=\dfrac{\cancel{2}(3\pm\sqrt{7})}{\cancel{2}}
\\\\
u=3\pm\sqrt{7}
.\end{array}
