4cos(2x)-6cos(x)+5=4(2cos2(x)-1)-6cos(x)+5=0,
8cos2(x)-4-6cos(x)+5=0,
8cos2(x)-6cos(x)+1=0=(2cos(x)-1)(4cos(x)-1).
So cos(x)=½ or ¼. x=π/3+2nπ, 1.3181+2nπ; also 2nπ-π/3, 2nπ-1.3181 (radians), where n is an integer.
In degrees this is: x=60°+360n°, 75.52°+360n°, 360n°-60°, 360n°-75.52°.
Decimals are approximate.