$a \triangle b = a^2 + b - \frac{a}{b}$

With $a = 5$ and $b = \frac{1}{2}$:

$= 25 + \frac{1}{2} - \frac{5}{1/2} = 25 + 0.5 - 10 = 15.5 = 15\tfrac{1}{2}$

Wait — let me recheck: $\frac{5}{1/2} = 10$.

$5^2 + \frac{1}{2} - 10 = 25.5 - 10 = 15.5$

But that's $15\frac{1}{2}$, which is choice D.