sixthroot x^5 = 9 * twelfthroot x^7 - 14*thirdroot x

Answer 1

x^5/6 = 9x^7/12 - 14x^1/3
x^10/12 - 9x^7/12 + 14x^4/12 = 0
x^4/12(x^6/12 - 9x^3/12 + 14) = 0
x^1/3 (x^1/4 -7)(x^1/4 - 2) = 0
x = 0,7^4,2^4

Answer 2

but if you plug in all 3 answers back to check for extraneous solutions, are any extraneous?