How would you solve the given equation?

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How would you solve the given equation?

Mathematics
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Is the fraction 1/3 the exponent of x?
Not sure, I honestly don't understand at all. here are the multiple choice answers if it helps? But I need the explanation on how to do it.
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I don't understand how that problem can have those answers.
The equation looks like this to me. \(\Large x - 7x^{\frac{1}{3}} + 6 = 0\)
Yea same here but not, but I don't know what the "-" sign is suppose to be?
To solve this equation (assuming this is the correct equation), Move the exponent term to the right, and cube both sides.
\(\Large x - 7x^{\frac{1}{3}} + 6 = 0\) \(\Large x + 6 = 7x^{\frac{1}{3}}\) \(\Large (x + 6)^3 = (7x^{\frac{1}{3}})^3\) \(\Large (x + 6)^3 = 343x\) \(\Large (x + 6)(x^2 + 12x + 36) = 343x\) \(\Large x^3 + 12x^2 + 36x + 6x^2 + 72x + 216 = 343x\) \(\Large x^3 + 18x^2 + 108x + 216 = 343x\) \(\Large x^3 + 18x^2 - 235x + 216 = 0\)
\[7x ^{\frac{ 1 }{ 3 }} = x+6\]\[343x = x^3+18x^2+108x+216\]\[x^3+18x^2-235x+216=0\]But neither 216 nor -216 is a root. Could there be something wrong with the question?
well plugging in x = 1 I do have the equation going to 0 .
maybe rational toot test might work?!
wow something is off with the question...
|dw:1439178737323:dw|
and then factoring that (x-8)(x+27) so (x-1)(x-8)(x+27) or x = 1,8,-27 where the heck does x = 216 or x = -216 come into play?
OMG I ANSWERED MY OWN QUESTION x = -216 x = (-27)(8)
those dummies combined the x = -216 -___________- the answer is actually x = 1, x = 8, x = -27 but they thought it was a great idea to combine x =8 and x -27 together to make x=(8)(-27) = -216 X_X!
So with my choices given would it be c?
yeah.. and if they knock points off, you can complain and use my work as evidence to show how wrong they are.
Ok will, thank you once again!

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