8cotx - 3tanx - 2 = 0
8/tanx -3tanx - 2 = 0
Multiply tan x on both sides,
this gives:
8 - 3 tan²x - 2tanx = 0
3tan²x+ 2tanx - 8 = 0
solve the quadratic
(3 tan x - 4) ( tan x + 2)
tan x = 4/3 and tan x = -2
x = 53.1 , -63.4
therefore,
x = 53.1, 116.6
but in the range,
x = 53.1 only