Final answer:
Unable to solve the expression 4x²=-4y² within the current context as it involves two variables without a clear relationship between them. The quadratic formula applies to equations of the form at² + bt + c = 0 but cannot be used directly in this multi-variable scenario without additional information.
Step-by-step explanation:
The student has the algebraic expression 4x²=-4y² which seems to relate to the ratios provided: 16y/√2 :: 12x. This looks like a proportion, but the question format is not clear. However, if we try to solve the given expression explicitly using the quadratic formula with the format ax² + bx + c = 0, it doesn't exactly fit since we have two variables (x and y) and not a standard quadratic equation.
Without additional context or equations to relate x and y, or to solve for one in terms of the other, we cannot definitively solve for either variable based on the given expression alone. Thus, it's not possible to confidently select from the given options (a, b, c, and d) without further information to establish a relationship between x and y.
When using the quadratic formula, it is generally applied to expressions of the form at² + bt + c = 0, where the solutions are found by substituting the appropriate values for a, b, and c into the quadratic formula, yielding the roots of the equation.