The quadratic $x^2-4x-14=3x+16$ has two solutions.  What is the sum of these solutions?
To find the sum of the solutions of a quadratic equation, I don't need to actually solve for each solution individually. Instead, I can use the fact that the sum of the solutions of a quadratic equation of the form $ax^2+bx+c=0$ is equal to $-\frac{b}{a}$. To use this formula, I need to first write the given equation in standard form: $x^2-4x-14=3x+16 \implies x^2-7x-30=0$. Now, I can see that $a=1$, $b=-7$, and $c=-30$. Therefore, the sum of the solutions is $-\frac{-7}{1}=7$. 