Verified answer

6x ^ (2/3) - 7x^ (1/3) - 24 =0

=> 6x ^ ( (1/3) )² - 7x^ (1/3) - 24 =0

let y = x ^ (1/3) which = ∛x

=> 6y² - 7y - 24 =0

=> 6y² - 16y+ 9y - 24 =0

=>2y( 3y -8) + 3( 3y -8) =0

=> (2y +3) ( 3y -8) = 0

=> either y = -3/2 (rejected since answer to the power of an integer cannot be negative)

or y = 8/3

=> y = 8/3

Now we should not forget that we used y = x^ (1/3) to calculate x

=> x^ (1/3) = 8/3

Cube both sides

=> x = ( 8/3)³

=> x = 8³ / 3³

=> x= 512 /27 <---