3cos^2x+10cosx+3=0 factor as
(3cosx + 1) ( cosx + 3) = 0 set both factors to 0
The second factor will have no solution
For the first factor we have......
3cosx + 1 = 0 subtract 1 from both sides
3cosx = -1 divide both sides by 3
cosx = -1/3 take the cosine inverse
cos (-1/3) = x = about 109.47° + n*2pi where n is an integer
and at about 250.529° + n*2pi where n is an integer