Solving a Physics Problem: Struggling with Algebra

[GreenPrint]

Homework Statement

Ok this was a physics problem...

I'm having a hard time with the algebra part

Homework Equations

solve for X

7.35E22/(3.84403E8 - X)^2 = 5.98E24/X^2

The Attempt at a Solution

i have got down to this and I think it is right but it might be wrong

0 = (7.35E22 X^2)/5.98E24 - X^2 + 2(3.84403E8)X - (3.84403E8)^2

 

[Mentallic]

Rather than dealing with all those long and annoying numbers, let's assign letters to stand for them, and we can substitute back after all the algebra is done.

Let:
$$A=7.35x10^{22}$$
$$B=3.84403x10^8$$
$$C=5.98x10^{24}$$

So now we have $$\frac{A}{(B-X)^2}=\frac{C}{X^2}$$

You want to get rid of the fractions, so you need to multiply by the higher common factor, which is $X^2(B-X)^2$

Then you'll get $$AX^2=C(B-X)^2$$

Now you need to expand, move everything to one side and let the equation = 0 and collect like terms. You should get it in the form $mx^2+nx+p=0$ where m, n and p are all some constant, and x is the variable that you're trying to solve.

Now you can apply the quadratic formula.