Question 1053562
Let {{{ z = sin(x) }}}
{{{ 5*(sin(x))^2 - sin(x) - 2 = 0 }}}
{{{ 5z^2 - z - 2 = 0 }}}
Use quadratic formula
{{{ z = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}} 
{{{ a = 5 }}}
{{{ b = -1 }}}
{{{ c = -2 }}}
{{{ z = (-(-1) +- sqrt( (-1)^2 - 4*5*(-2) ))/(2*5) }}} 
{{{ z = ( 1 +- sqrt( 1 + 40 ))/10 }}} 
{{{ z = ( 1 +- 6.4031 ) / 10 }}}
{{{ z = 7.4031/10 }}}
{{{ z = .7403 }}}
and
{{{ z = -5.4031/10 }}}
{{{ z = -.5403 }}}
-------------------------
{{{ sin(x) = .7403 }}}
{{{ x = arc sin( .7403 ) }}}
{{{ x = 47.757 }}} degrees
and
{{{ x = arc sin( -.5403 ) }}}
{{{ x = -32.704 }}} degrees
-------------------------
Aso for {{{ x }}}, I get:
{{{ x = 180 - 47.757 }}}
{{{ x = 132.243 }}} 
( this is 2nd quadrant where sin is also positive )
and
{{{ x = -180 -( -32.704 ) }}}
{{{ x = -180 + 32.704 }}}
{{{ x = -147.296 }}}
( this is 3rd quadrant where sin is also negative )
--------------------------
I think you need all 4 of these answers
Get another opinion, also