Answer
$1, -9$
Work Step by Step
For the equation $x^2 +8x -9= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=1, \quad b=8, \quad c=-9
.$$
That is, $$ x=\frac{-8 \pm \sqrt{64+36}}{2 }=\frac{-8 \pm10}{2 }= 1, \ or, \ -9
.$$
Check the result:
$$
1^2+8-9=9-9=0, \quad
9^2-72-9=9-9=0.
$$
