The delta of a quadratic is its discriminant, which in this case is:
(m-1)2-4(m+2)=m2-2m+1-4m-8=m2-6m-7=(m-7)(m+1).
Delta<0 (negative) when -1<m<7 and delta≥0 (positive) when m≤-1 or m≥7.
When m=7 or -1, the quadratic has two distinct roots.
The roots of x2-6x+9=0=(x-3)2 or x2+2x+1=0=(x+1)2, making the roots x=3 or -1.
That is: x=(m-1)/2 because delta=0.