Determine all the values of x if 2tan^2x-tanx-1=0

We have to solve 2(tan x)^x - tan x - 1 =
0

Now 2 (tan x)^2 - tan x - 1 =
0

=> 2 (tan x)^2 - 2tan x + tan x - 1 =
0

=> 2 tan x( tan x -1) +1 (tan x -1)
=0

=> (2 tan x +1) (tan x-1)
=0

Therefore tan x = -1/2 or tan x
=1

If tan x = 1 , x = 45
degree

If tan x = -1/2 , x = -26.56
degree

Therefore the solutions are 45 degree
and -26.56 degree.