x^2 -6x +14

x² - 6x + 14 = 0

Discriminant D = b²-4ac

= 62 - 4(1)(14) = 36 - 56 = -20

Since the Discriminant D is negative, this equation has no real solutions. It has only imaginary solutions.

square root(D) = sqrt(-20) = 2i sqrt(5)

x= (-b + sqrt(D))/2a , (-b - sqrt(D))/2a

or, x = (6 + 2i sqrt(5))/2 , (6- 2i sqrt(5))/2

or, x = 3 + i sqrt(5), 3 - i sqrt(5) are the imaginary solutions.

(If you have not studied complex numbers, leave out the part after the 4th line)

this equation does not have real roots

D<0

it will be 6+/_iroot20