Decide what is t if quadratic equation has two equal roots. x^2+(2t-4)*x+t+1=0

For the given quadratic to have 2 equal roots, the
discriminant delta is cancelling out.

delta = (2t-4)^2 -
4(t+1)

delta = 0

We'll expand
the square and we'll remove the brackets in the expression of
delta:

4t^2 - 16t + 16 - 4t - 4 =
0

We'll combine like
terms:

4t^2 - 20t + 12 =
0

We'll divide by 4:

t^2 - 5t
+ 3 = 0

We'll have to determine the roots of the expression
t^2 - 5t + 3 = 0

t^2 - 5t + 3 =
0

We'll apply the quadratic
formula:

t1 = [5+sqrt(25 -
12)]/2

t1 = (5 + sqrt13)/2

t2
= (5 - sqrt13)/2

The values of t, for the
given quadratic to have equal roots, are: {(5 - sqrt13)/2 ; (5 +
sqrt13)/2}.