We have x 2 +3x+9=0 .
Any equation of the form a x 2 +bx+c=0 has the solution
x= −b± D 2a
Here, D= b 2 −4ac is called the discriminant of the quadratic equation.
Therefore,
x= −3± −27 2 = −3± 27 i 2
Thus, x= −3± 27 i 2 .