4sin²x+cos²x+5sinx*cosx=0 |:cos²x≠0
4sin²x/cos²x+cos²x/cos²x+5sinx*cosx/cos²x=0
4tg²x+1+5tgx=0
tgx=y
4y²+5y+1=0
a=4, b=5, c=1
D=5²-4*4*1=9
y₁,₂=(-b+-√D)/(2*a)
y₁=(-5-3)/8, y₁=-1
y₂=(-5+3)/8, y₂=-1/4
1. y=-1, tgx=-1, x₁=-πn, n∈Z
2. y=-1/4, tgx=-1/4, x₂=-arctg(1/4)+πn, n∈Z