# Solving the equation for y

1. Jan 16, 2014

### examorph

I have been trying to solve the following equation for the variable y:
https://imageshack.com/i/0r9khg
Where K and P are constants, I tried an online solver which gave me the following result:
https://imageshack.com/i/nq4qm6g

I attempted to solve for this by adding the -1/2(n^2 t^2 y) to both sides and then dividing the -1/2(n^2 t^2) from both sides which left me with a big mess on the right, were the steps followed so far correct? Where would I go from here to solve for y?

Also, it has been suggested to me that this may require the use of the quadratic formula, is this correct?

Thanks.

2. Jan 16, 2014

### Staff: Mentor

Just move the -1/2(n^2 t^2 y) to the left side and factor out the y and from there it should be obvious...

3. Jan 16, 2014

### examorph

Thanks for the reply. I have tried this:
https://imageshack.com/i/mu2vb0g
When I divide both sides by the coefficient I get a large formula on the right hand side which does not match the final result shown by the solver, I had also been told that the quadratic formula is required to solve this, could you please show me what I must do next?

4. Jan 16, 2014

### Ray Vickson

You have a simple equation of the form $y = A - By$, where
$$A = \frac{kt}{p}-\frac{k \sin(pt)}{p^2} \text{ and } B = \frac{n^2 t^2}{2}$$
Solving for y ought to be simple for you, without recourse to an on-line solver. Anyway, the solution given to you by the on-line solver is wrong. Are you sure you submitted the right equation?