Answer
$x=-6,6$
Work Step by Step
Isolate the variable factor on one side, and then take the $n$th root of both sides to solve for the variable. If the root is even, there will be a positive and negative answer. If the root is odd and the other side is negative, there is only a negative answer.
$-4x^8+2768=-6715696$
$-4x^8=-6718464$
$x^8=1679616$
$x=-6,6$