in the equation y = x^2-4x+5, the discriminate is positive (?) therefore there are two answers, yet my textbook says the discriminate is negative ??? help!

It is discriminant Not discrimante :)

\(y = x^2-4x+5\\ \triangle=b^2-4ac\\ \triangle=(-4)^2-4*1*5=16-20=-4<0\\\)

The discriminant is -4 which is negative so there are no real roots :)