There are two distinct solutions x to the equation 18 + 5x^2 = 30x. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?
Moving all the terms to the left side and arranging gives $5x^2+30x+18=0$
Using the quadratic formula, you get $x=\frac{-30+\sqrt{30^2-4(18)(5)}}{2(5)}$ and $x=\frac{-30-\sqrt{30^2-4(18)(5)}}{2(5)}$, which simplifies to
$x=-3+\frac{3\sqrt{15}}{5}$ and $x=-3-\frac{3\sqrt{15}}{5}$.
When rounded, these give $x=-3+2=-1$ and $x=-3-2=-5$.
When multiplied, these give $-1*-5=\boxed{5}$