Final answer:
The question seemed to ask for a solution for y in an equation, but the provided equation is not clear or standard, making it impossible to solve for y without additional information or correction.
Step-by-step explanation:
The student has provided an equation and the task is to solve for y. The equation given is: 1/3 * y² - 18y + 9 - 2y⁻². However, there seems to be a typo or lacking information as the equation is not correctly set up for solving for y. We usually expect a polynomial equation or a clear expression that can be isolated to one side of the equation to find the value of y. With the given terms, it's not strictly possible to 'solve for y' without additional context or restructuring the equation into a standard form.
To find values of y, we would need an equation of the form y = (some expression), or a polynomial equal to zero that we could factor or use the quadratic formula to solve.