Question 1028339
2sinx + 4cos2x  = 3 <==> {{{2sinx +4(1-2sin^2(x)) = 3}}}

<==> {{{0 = 8sin^2(x)-2sinx - 1}}} <==> {{{0=(4sinx+1)(2sinx-1)}}}

==> {{{sinx = -1/4}}} or {{{sinx = 1/2}}}

==> {{{x = 360^o + sin^-1(-1/4)}}}, or {{{180^o - sin^-1(-1/4)}}} from the first equation, and 

x = {{{30^o}}} or {{{150^o}}} from the second equation.

To nearest degree, the answers are {{{345^o}}}, {{{194^o}}}, {{{30^o}}} or {{{150^o}}}.