Question 596611
-2x^2+6x+9=0 

its quadratic so either use the quadratic formula {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
or complete the square....

factor out -2

-2(x^2-3x-9/2)=0 

x^2-3x=9/2     
add 9/4 to both sides  
 x^2-3x+9/4=9/2 + 9/4

x^2-3x+9/4=[x-(3/2)]^2    
so  [x-(3/2)]^2 = 27/4

sqrt both sides x-(3/2) = (+-)sqrt(27/4)

sqrt(27/4)=3sqrt3/2

add 3/2 to both sides.....

x=[3(+-)3sqrt3]/2