A boy tried to align 480 coins in the shape of a triangle, with one coin in the first row, two coins in the second row, and so on. At the end of the attempt, 15 coins were left over. How many rows does this triangle have?
Suppose the triangle is formed by $n$ rows, then $1+2+3+\cdots+n$ coins were used, that is,

$$
\frac{1}{2} n(n+1)=1+2+\cdots+n=480-15=465
$$

which gives $n^{2}+n-930=0$. Solving this equation, we get

$$
n=\frac{-1 \pm \sqrt{1+4 \times 930}}{2}=\frac{-1 \pm 61}{2}
$$

Since $n=30$ is the only positive solution to this equation, the triangle has 30 rows.