Answer
Center is at (-4, 3, -1) and the radius is 3
Work Step by Step
$x^{2} + y^{2} + z^{2} + 8x - 6y + 2z = -17 $
$x^{2} + 8x + y^{2} - 6y + z^{2} + 2z = -17 $
$x^{2} + 8x +16 + y^{2} - 6y + 9 + z^{2} + 2z + 1 = -17 + 16 + 9 + 1 $
$(x + 4)^{2} + (y-3)^{2} + (z+1)^{2} = 9 $
This is indeed a sphere, the center is at (-4, 3, -1) and the radius is 3
