Answer
$n=3$
Work Step by Step
First square both sides: $n^2=24-5n$
Then move the $24-5n$ to the left-hand side to create a quadratic: $n^2+5n-24=0$
Use the quadratic formula to solve for possible values of $n$:
The quadratic formula states that for a quadratic $ax^2+bx+c$, the two possible roots take the form $\frac{-b+\sqrt{b^2-4ac}}{2a}$ or $\frac{-b-\sqrt{b^2-4ac}}{2a}$.
We see that the two possible roots of our equation are $\frac{-5+\sqrt{121}}{2}=3$ and $\frac{-5-\sqrt{121}}{2} = -8$.
Looking back at our original equation, we see that $n$ is the square root of a number. Because the square root of a number cannot be negative, we see that $n=3$ is the only solution to this equation.
