#### Answer

$x=6$

#### 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.
$-\frac{1}{3}x^7+345=-92967$
$-\frac{1}{3}x^7=-93312$
$x^7=279936$
$x=6$