Question

3x^4=648x
someone help please im so confused. i am trying to find the solution set?

Answer 1

3x^4 - 648x = 0
divide by 3

x^4 - 216x = 0
x(x^3 - 216)=0
x = 0 or x^3-216=0

if you want only real solutions
then from x^3=216
x = 6

however, if you want complex roots at well .....

x^3 - 216 = (x-6)(x^2 + 6x + 36) = 0
x= 6 , we already know that
or
x = (-6 ±√-108)/2
= (-6 ± 6i√3)/2
= -3 ± 3i√3

so x = 0 , 6 , -3±3i√3