Tan^2x + 5tanx + 3=0

Approximate to four decimal places the solutions for x,

0 less than or equal to x<2pi

Tan^2 x + 5tan x + 3 = 0

Let tan x = m, then

m^2 + 5m + 3 = 0

m^2 + 5m + 25/4 = - 3 + 25/4 = 13/4

(m + 5/2) ^2 = 13/4

m + 5/2 = + or - sqrt (13) / 2

m = (√13 - 5) / 2 or (-√13 - 5) / 2

tan x = (√13 - 5) / 2 or (-√13 - 5) / 2

x = arctan ((√13 - 5) / 2) or arctan ((-√13 - 5) / 2)

x = 103.0837, 145.1149, 283.0837, 325.1149