For a quadratic equation written in general form
#ax^2 + bx + c = 0#,
the discriminant is defined as
#Delta = b^2 - 4 * a * c#
In your case, the quadratic looks like this
#3x^2 + 6x +5 = 0#,
which means that you have
#{(a=3), (b=6), (c=5) :}#
The discriminant will thus be equal to
#Delta = 6^2 - 4 * 3 * 5#
#Delta = 36 - 60 = color(green)(-24)#
When #Delta<0#, the equation has no real solutions. It does have two distinct complex solutions derived from the general form
#x_(1,2) = (-b +- sqrt(Delta))/(2a)#
which in this case becomes
#x_(1,2) = (-b +- isqrt(-Delta))/(2a)#, when #Delta<0#.
In your case, these two solutions are
#x_(1,2) = (-6 +- sqrt(-24))/(2 * 3)#
#x_(1,2) = (-6 +- isqrt(24))/6 = (-6 +- 2isqrt(6))/6 = {(x_1 = (-3 - isqrt(6))/3), (x_2 = (-3 + isqrt(6))/3) :}#