Question 364906
{{{2x^2/3 - 8x^1/3 + 15 = 0}}} | let {{{x = y^3}}}
  
{{{2y^2 - 8y + 15 = 0 = 2 ( y^2 - 4y) + 15 = 2((y-2)^2-4) + 15 = 2(y-2)^2 + 7}}}
 
{{{2(y-2)^2 = -7}}}, negative hence there are no real solutions 
 
(Or discriminant = 8^2 - 4*15*2 < 0)

the complex solutions are : y = 2 +/- i*Sqrt(7/2)
 
and x = [2 +/- i*Sqrt(7/2)]^(1/3)
 
to put x on the form a + ib, for example : |y| = Sqrt(4 + 7/2) = Sqrt(15/2)
 
writing then : y = |y|exp(it), we find t = atg(7/8)
 
y^(1/3)=Sqrt(15/2)^(1/3)*exp(it/3 + 2*pi/3 *m), m=0, 1, 2