Find all the solutions of the equation in the interval {o,2pi)

Question

5sqrt3 tan x+3=8sqrt3 tan x

Answer 1

5√3 tanx + 3 = 8√3 tanx
3√3tanx = 3
√3 tanx = 1
tanx = 1/√3
x = π/6 in quadrant I
or
x = π + π/6 or 7π/6 in quadrant III

x = π/6 , 6π/6

Answer 2

(2sqrt3+8)(5sqrt3-4)