Answer
Since the discriminant is a positive number that is not a perfect square, there are $2$ different irrational solutions.
Work Step by Step
$ x^{2}-8x+1=0\qquad$.... $a=1,\ b=-8,\ c=1$
$ b^{2}-4ac\qquad$....substitute $b$ for $-8,\ a$ for $1$ and $c$ for $1$
$=(-8)^{2}-4\cdot 1\cdot 1$
$=64-4$
$=60$
