solve equation for the exact solutions if possible put answer in degrees.

Question

2tanx/3-tan^2x=1

Answer 1

I have a suspicion that you meant
2tanx/(3 - tan^2x) = 1
then
2tanx = 3 - tan^2x
tan^2x + 2tanx - 3 = 0
(tanx + 3)(tanx - 1) = 0
tanx = -3 or tanx = 1

if tanx = -3, x must be in II or IV by the CAST rule
x = 108.4° or 288.4°

if x = 1, then x must be in I or III
x = 45° or x = 225°