Hello!
6x^2 + 13x + 6 has coefficients a = 6, b = 13 and c = 6. The discriminant,
b^2 - 4ac, is therefore 13^2 - 4(6)(6) = 169 - 144 = 25.
Because the discriminant is positive, we have two unequal, real roots. They are:
-13 plus or minus √25
x = -----------------------------------
2(6)
-13 plus or minus 5
= --------------------------------
12
and these come out to -8/12 and -18/12, reductable to -2/3 and -3/2. I'd prefer to state "two real, rational, distinct roots," but "double root" is OK.
