Genral solution of:

2tan x + 3=0

Solve for x if:
2tan x +3 =0 and x E[-180;180]

1 answer

2tanx = -3
tanx = -3/2
x must be in quadrants II or IV
angle in standard position , tan^-1 (3/2) = 56.3°

so x = 180-56.3 = 123.7° or
x = 360 - 56.3 = 303.7°

general solution
x = 123.7 + 180k or x = 303.7 + 180k, where k is an integer.

for the second part, 303.7 is clearly too large
but 123.7-180 = -56.3° will work

check: 2tan (-56.3) + 3 = 0.0011 , close enough