1. x^4 -52x + 576 = 0
This has no real solutions.........see the graph, here :https://www.desmos.com/calculator/dniadv9jnx
2. x^3 = 216
x^3 - 216 = 0 factor as a difference of cubes
(x -6) (x^2 + 6x + 36) = 0
Setting each factor to 0, it's clear that x = 6 is the real solution
Setting x^2 + 6x + 36 to 0 and using the quadratic formula we obtain two non-real solutions :
-3-3 i sqrt(3) and -3+3 i sqrt(3) [the last answer ]