2m-m^2+1=2(m^2-2m)^2

令m^2-2m=a
则-a+1=2a^2
2a^2+a-1=0
(2a-1)(a+1)=0
a=1/2,a=-1
m^2-2m=1/2
(m-1)^2=3/2
m-1=±√6/2
m=1±√6/2
m^2-2m=-1
(m-1)^2=0
m=1
所以m=(2-√6)/2,m=(2+√6)/2,m=1