solve for x exactly between 0<x<2pi

Question

sec^2(x)+7tan(x)=5tan(x)

Answer 1

sec²x + 7tanx = 5tanx

(1 + tan²x) + 7tanx = 5tanx

tan²x + 2tanx + 1 = 0

(tanx + 1)² = 0

tanx = -1

x = 3π/4 or 7π/4

Answer 2

So then

sec^2 + 2 tan = 0

multiplies both sides by cos^2

1 + 2 sin cos = 0

1 + 2 sin(2x) = 0

sin(2x) = -1/2

Let U = 2x

sin U = -1/2

sine is negative in quadrants 3 and 4

U = 210 and 330 degrees

2x=210 and 2x=330

x = 105 and x= 165 degrees

change them to radians