Rewriting Equations

[JokerDriver]

Hello everyone,

I was given a problem in my math textbook, which is for my Algebra 2 class. It is in the section for "Rewriting Equations" and it says:

"Solve the formula: t = a + n (n - 1 )d for n"

I got this far but I am stuck at a certain point, which I was hoping someone could help me finish the equation, as I already have half of it but this ending part is what is getting me now.
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I started off by moving a over to the other side to get:

I am now dividing by d to get:

I have expanded the right hand side and got:

Now I am adding

to both sides to get:

Now I have a common denominator to add the fractions, and am factoring the right hand side to get:

Now, this is where I am stuck at... anyone who can help me, thanks a lot.

 

[Denis]

"Solve the formula: t = a + n (n - 1 )d for n"

equation really is:
t = a + dn(n - 1 )
complete the multiplication:
t = a + dn^2 - dn
set to equal 0:
dn^2 - dn + a - t = 0

Now solve for n using the quadratic formula.

 

[Loren]

Now I have a common denominator to add the fractions, and am factoring the right hand side to get:

Your method of completing the square will yield the same result as going to the quadratic formula. Your work is good as far as you got. From here combine the fractions on the left. Then multiply both numerator and denominator by d. That will give you a perfect square in the denominator. Your next step will be to take the square root of both sides and from their, clean it up a little bit to get into the simplest form.