it starts going wrong when you go from

(a-t/2)²=(b-t/2)² TO (a-t/2)=(b-t/2)

ex. suppose a=2 & b=-1 ==> t=1

(a-t/2)²=(2-1/2)²=9/4=(-1-1/2)²=(b-t/2)²

But

(a-t/2)=3/2 NOT= -3/2=(b-t/2)