I often find it easier to write the equation this way 5x^2 -18x-8=0 understanding that x is really sin x

(5x+2)(x-4)=0. X=4. This is extraneous as the range of sin x is from -1 to +1

5x=-2 x=-.4 gives you sinx =-.4 Take inverse sin to get x= -23.58 degrees which is the same as + 336.42 which is in quadrant 4

Sin is also negative in quadrant 3 so this would be 180+23.56= 203.58