How do I solve this equation?

Question

I have an equation, where I need to find n, that I need help solving.

I already cheated a little bit by using a CAS (Maple) to solve the equation, so i know what the result should be, but I need to know how to get the to result without using a CAS.

The equation:

$$\frac{2400}{(n-5)}= \frac{2400}{n} + 40$$

Here is what I have done so far, but I'm not sure how to proceed:

Answer 1

So the CAS tells you how to transform it into a quadratic equation. Now to solve $40n^2 -200n-12000=0$:

Divide by $40$: $n^2 -5n-300=0$

Factorize: $(n-20)(n+15)=0$ (or use quadratic formula $\frac{5\pm \sqrt{(-5)^2-4(-300)}}{2}$)

So $n=20$ or $-15$.

Answer 2

You have already rewritten it to a quadratic, you just need to move the last term to have it in standard form allowing you to use the formula for the roots of a quadratic.