If x^2 - 5x + 8 = 0 find the roots of the equartion. Are the roots real number?

Let f(x) = x^2 - 5x + 8 =
0

Then, we need to find the roots of the equation
f(x).

First, let us calculate delta to determine if the
roots are real or complex.

We know that delta = b^2 -
4ac

==> If delta < 0 , then the roots are
complex.

==> If delta = 0, then the function has one
real root.

==> If delta > 0 , then the
function has 2 real roots.

==> delta = 25 - 4*1*8 =
25 - 32 = -7.

Then, delta < 
0..

==> The function has 2 real
roots.

==> x1= ( -b + sqrt(delta) /
2a

==> x1= ( 5 + sqrt(-7) /2 =
(5+sqrt7*i)/2

==> x2=
(5-sqrt7*i)/2