Solve for x : 2x2/3-x1/3 = 28

Question : Solve for x : 2x^2/3-x^1/3 = 28

Doubt by Charu 

Solution :

2x^2/3-x^1/3 = 28
2(x^1/3)²-(x^1/3)=28

Let x^1/3 = y

2y²-y=28
2y²-y-28=0
2y2-(8-7)y-28=0
2y²-8y+7y-28=0
2y(y-4)+7(y-4)=0
(2y+7)(y-4)=0

2y+7=0
2y=-7
y=-7/2

x^1/3=-7/2
Taking cube both sides
[x^1/3]³=[-7/2]³
x = -343/8

y-4=0
y=4

x1/3 = 4
Taking cube both sides
[x^1/3] ³=(4)³
x = 64

∴ x =-343/8 or x=64