Help quadratic equations are so hard
The quadratic equation $x^2-5x+t =3x$ has only positive integer roots. Find the average of all distinct possible values of $t$.
Rearrange as
x^2 - 8x + t = 0
Possible factors
roots t
(x - 7) ( x - 1) 1 , 7 7
(x - 2) ( x - 6) 2, 6 12
(x - 3) ( x - 5) 3, 5 15
(x - 4) (x - 4) 4 16
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50 = sum of t's
Average of t's = 50 / 4 = 12.5
+1348 
