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

May 26, 2015

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 (${x}_{0} = - \frac{b}{2 a}$)
If $\Delta > 0$ then there are 2 real solutions which you can calculate using:
${x}_{1} = \frac{- b - \sqrt{\Delta}}{2 a}$ and ${x}_{2} = \frac{- b + \sqrt{\Delta}}{2 a}$