\(x^2-14x+48=0 \\ \\
a=1 \\ b=-14 \\ c=48 \\ b^2-4ac=(-14)^2-4 \times 1 \times 48=196+192=4 \\ \\
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-14) \pm \sqrt{4}}{2 \times 1}=\frac{14 \pm 2}{2}=\frac{2(7 \pm 1)}{2}=7 \pm 1 \\
x=7-1 \ \lor \ x=7+1 \\
x=6 \ \lor \ x=8 \\
\boxed{x=6 \hbox{ or } x=8}\)
