Verified answer

Here's your equation: Profit cartel/ (1-δ) ≥ profit deviation + δ(profit Nash eq. / (1-δ))

These are your designations:

Profit cartel = ((a-c)^2)/8b

Profit Nash eq. = ((a-c)^2)/9b

Profit deviation = (9(a-c)^2)/64b

Make these changes:

Profit cartel = A

Profit Nash eq. = B

Profit deviation = C

Your equation ===> A / ( 1 - δ ) ≥ C + δ( B / (1 - δ) )

Now you have an equation you can deal with, and it's just simple, and straightforward algebra.

=> A / ( 1 - δ ) ≥ C + δ( B / (1 - δ) )

=> A / ( 1 - δ ) ≥ C + δB / (1 - δ) )

=> A ≥ C(1 - δ) + δB

=> A ≥ C - Cδ + δB

=> δ( B - C ) ≥ C - A

=> δ ≥ ( C - A ) / ( B - C )

Much easier to work with it in this way, now just put back in for A, B & C and you're done.