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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
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