SOLUTION: Please help me solve this problem: {{{2^((2/3)x+1)-3(2^((1/3)x))-20=0}}}

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Question 141877This question is from textbook Algebra and Trigonometry
: Please help me solve this problem: 2%5E%28%282%2F3%29x%2B1%29-3%282%5E%28%281%2F3%29x%29%29-20=0 This question is from textbook Algebra and Trigonometry

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let y=2^((1/3)x) __ substituting __ 2y^2-3y-20=0

factoring __ (2y+5)(y-4)=0

2y+5=0 __ y=-5/2 __ substituting __ 2^((1/3)x)=-5/2
__ cannot raise a positive number to a power and get a negative result so NO SOLUTION

y-4=0 __ y=4 __ substituting __ 2^((1/3)x)=2^2 __ (1/3)x=2 __ x=6