Are you a handshaker?

We can use the handshake formula. Let $n$ be the number of people.

$\text{number of handshakes}=\dfrac{n}{2}(n-1)$

$28=\dfrac{n}{2}(n-1)$

$n^2-n-56=0$

Using the quadratic formula, $n=\boxed{8}$ .

$\begin{aligned} \dbinom{n}{2} & = 28\\ \\ \dfrac{n(n-1)}{2} & = 28\\ \\ n^2 - n & = 56\\ n^2 - n - 56 & = 0\\ (n - 8)(n + 7) & = 0\\ n & = 8, {\cancel{-7}} \ (\text{number of people cannot be negative})\\ \\ \therefore n & = \color{#3D99F6}{\boxed{8}} \end{aligned}$

There is a formula for the total of handshakes which is $\frac{n(n-1)}{2}= \text{total number of handshakes, where n is the number of people}$ . Therefore, we can solve for $n$ using this equation $\frac{n(n-1)}{2}=28\implies n^2-n-56=0 \implies (n-8)(n+7)=0$ which tells us that $\boxed{n=8}$