Question

How to use the discriminant to find out what type of solutions the equation has for `x^2+3x+8=0`?

Answer 1

This equation has no real solutions.

The rule is that:

If `Delta<0` then there are no real solutions (there are 2 complex solutions)
If `Delta=0` then there is one real solution (`x_0=-b/(2a)`)
If `Delta>0` then there are 2 real solutions which you can calculate using:
`x_1=(-b-sqrt(Delta))/(2a)` and `x_2=(-b+sqrt(Delta))/(2a)`