Solve for a over the real numbers:
a^2/3 - 1/a = a^2/6
Bring a^2/3 - 1/a together using the common denominator 3 a:
(a^3 - 3)/(3 a) = a^2/6
Cross multiply:
6 (a^3 - 3) = 3 a^3
Expand out terms of the left hand side:
6 a^3 - 18 = 3 a^3
Subtract 3 a^3 - 18 from both sides:
3 a^3 = 18
Divide both sides by 3:
a^3 = 6
Take cube roots of both sides:
Answer: a = 6^(1/3)