Question 169·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

The equation has $0$ on the right, so a solution makes its left side zero. Type $y=x^2-2x-48$ in Desmos, replacing every $n$ with $x$ because Desmos uses $x$ on its horizontal axis. The curve crosses that axis at two x-intercepts.

Click both intercepts. Desmos labels them $(-6,0)$ and $(8,0)$. Their horizontal coordinates give $n=-6$ and $n=8$; the $0$ is the graph's height, not the value of $n$. Only $n=8$ is positive, so it answers the question. Choice B.

To factor $n^2-2n-48$, look for two numbers whose product is $-48$ and whose sum is $-2$, the number in front of $n$. Those numbers are $-8$ and $6$, so:

Put the factored expression into the equation: $(n-8)(n+6)=0$. The zero-product property says a product is zero only if at least one factor is zero, so:

Solve each factor equation. Add $8$ to the first: $n=8$. Subtract $6$ from the second:

Both values solve the equation, but positive means greater than $0$. So $n=8$ is the positive solution. Choice B.