I need some math help. (in Off-topic)

I'm usually really good at math, but I'm just kindof having a brain glitch right now, so any help would be appreciated. I need help solving this problem:

If w = r +8 / (2r - 9) then r = what in terms of w?

is it (r+8)/(2r-9) or r + (8/(2r-9))?

w should = 8/9r

(r+8)/(2r-9) Sorry for the confusion

w = (r+8)/(2r-9)
(2r-9)w = r+8
2rw - 9w = r + 8
2rw - r = 8 - 9w
r(2w - 1) = 8 - 9w
r = (2w-1)/(8-9w)

Pk, I think you forgot to flip a sign when you transferred the 9w.

w = r +8 / (2r - 9)

(2r-9)w=r+8

2rw-9w=r+8

2rw-r=8+9w

r(2w-1)=8+9w

r=(8+9w)/(2w-1)

w = (r+8)/(2r-9)
(2r-9)w = r+8
2rw - 9w = r + 8
2rw - r = 8 + 9w
r(2w - 1) = 8 + 9w
r = (2w-1)/(8+9w)

sorry for mixing up the signs.

and the last line was wrong as well.
almaisky was right.

Yeah I noticed the error, no big deal PK. I'm just an idiot and for some reason the thought "use the distributive property" didn't go through my head once.

Hmm, how would you find r in terms of w for

w = r + (8 / (2r - 9) ) ?

w = r + 8/(2r-9)
2rw - 9w = 2r^2 - 9r + 8
2r^2 -9r -2rw +9w + 8 = 0

sub into ar^2 + br + c = 0 (solve for quadratic, which the formula I forgot)
a = 2
b = -9 - 2w
c = 9w + 8

I think it is something like r =[ -b ﾱ sqrt(b^2 - 4ac) ] / 2a

so r = [(9+2w) ﾱ sqrt(9+36w+w^2 - 72w -64)]/4

the weird symbol is "plus or minus"

so r = [(9+2w) ﾱ sqrt(81+36w+w^2 - 72w -64)]/4 I expanded the (9+2w)^2 part wrong in my head....