Verified answer

(3x-6)/2x^2=((x-2x^2)/(2-x))-2

(3x-6)(2-x)=(x-2x^2)2x^2-2*2x^2*(2-x)

6x-3x^2-12+6x=2x^3-4x^2-8x^2+4x^3

6x^3-9x^2-12x+12=0

2x^3-3x^2-4x+4=0

(x-2)(2x^2+x-2)=0

1.   x-2=0 => x=2

2. 2x^2+x-2=0

   D=b^2-4ac=1+16=17

   x1=(-1+sqrt(17))/4

   x2=(-1-sqrt(17))/4