Vectors question > < Please help!!

Two points A(2,-3) and B(a, -2a) are such that vector AB is a unit vector. Calculate the possible values of a.

Please help me!

Thank you so much in advance (:

Vector AB is AB= B-A
AB= (a-2, -2a+3)
If it is a unit vector , IABI=1

IABI = sqrt ((a-2)^2+(-2a+3)^2
IABI = sqrt (a^2-4a+4+4a^2-12a+9)
IABI = sqrt ( 5a^2-16a+13) =1
5a^2-16a+13=1
5a^2-16a+12=0
a= (16+- sqrt (256-240)) / 10.

a= (16+- 4)/10
a1= 20/10 =2
a2=12/10 =6/5