Question

Solve 2cos^2x+5cosx+2=0

Answer 1

$2cos^2x+5cosx+2=0\\ x\in\\ \Delta=b^2-4ac\\ \Delta=9\\ \sqrt{\Delta}=3\\ cosx=1\\ or\\ cosx=-6\\ -6\notin$

Then using trygonometric table or a graph we read that:
$cosx=1\Leftrightarrow(x)=0$

Period of cosinus function = 2π
So the last answer is $x=0+2k\pi$