SOLUTION: Find all the real solutions of the following equation as a quadratic equation. 6n^2/3 + n^1/3 - 15 = 0

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Question 465299: Find all the real solutions of the following equation as a quadratic equation.
6n^2/3 + n^1/3 - 15 = 0
Answer by lwsshak3(11628) About Me  (Show Source):
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Find all the real solutions of the following equation as a quadratic equation.
6n^2/3 + n^1/3 - 15 = 0
...
6n^2/3 + n^1/3 - 15 = 0
let x=n^1/3
x^2=n^2/3
..
6x^2+x-15=0
factor
(3x+5)(2x-3)=0
3x+5=0
x=-5/3
or
2x-3=0
x=3/2
..
n^1/3=-5/3
cube both sides
n=-125/27
..
n^1/3=3/2
cube both sides
n=27/8
ans:
n=-125/27 or 27/8