We need to find Darlene's age, let it be x. Also, let her sister age be y.
Okay, now using x and y notations we write what we know:
$\displaystyle x=y-3$ (Darlene is 3 years younger than her sister)
$\displaystyle x \cdot y=238$ (the product of their ages is 238)
$\displaystyle x=y-3 \Rightarrow x+3=y$
$\displaystyle x \cdot y=238 \Rightarrow x \cdot (x+3)=238 \Rightarrow x^2+3x=238 $
The answer is B.