Verified answer

6x^2-(7a+1)x-3a^2=4a+1

D=(11a+5)^2

x1=1/3(a-1)

x2=1/2(3a+1)

x^2+x+a=a^2

D=(1-2a)^2

x1=a-1

x2=-a

1/3(a-1)=a-1

a=1

1/3(a-1)=-a

a=1/4

1/2(3a-1)=a-1

a=-1

1/2(3a-1)=-a

a=1/5

a∈{-1,1/5,1/4,1}