The teacher will be very surprised to see your correct solution 😉
a*x^2 + b*x + c = 0
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (12) = -23
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
____ 5 I*\/ 23 x1 = - - -------- 2 2
____ 5 I*\/ 23 x2 = - + -------- 2 2
x2 = 5/2 + sqrt(23)*i/2
sum
____ ____ 5 I*\/ 23 5 I*\/ 23 - - -------- + - + -------- 2 2 2 2
=
5
product
/ ____\ / ____\ |5 I*\/ 23 | |5 I*\/ 23 | |- - --------|*|- + --------| \2 2 / \2 2 /
=
12
12
x1 = 2.5 + 2.39791576165636*i
x2 = 2.5 - 2.39791576165636*i
x2 = 2.5 - 2.39791576165636*i