Given:
[tex]x^2-6x-8=0[/tex]Required:
To find the solution of the given equation.
Explanation:
From the given equation,
[tex]\begin{gathered} a=1 \\ b=-6 \\ c=-8 \end{gathered}[/tex]Now
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Therefore,
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-8)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt{36+32}}{2} \\ \\ =\frac{6\pm\sqrt{68}}{2} \\ \\ =\frac{6\pm2\sqrt{17}}{2} \\ \\ =\frac{2(3\pm\sqrt{17)}}{2} \\ \\ =3\pm\sqrt{17} \end{gathered}[/tex]Final Answer:
The solutions are
[tex]x=3+\sqrt{17},3-\sqrt{17}[/tex]