How do I find the solutions of this equation?

Question

 Find all solutions of the equation t + 3 + 8/t =0 and express them in the form a + bi?

Input the solution with b<0:
The real number a equals ___ and the real number b equals ___.

Input the solution with b>0:
The real number a equals ___ and the real number b equals ___.

 

Answer 1

t + 3 + 8/t =0

t² + 3t + 8 = 0

Solution for the equation is 

a = 1 , b = 3 , c = 8

If Input the solution with b<0 ⇒   it is in the form of a +ib

The real number a equals  -3/2  and the real number b equals -(√ 23)/2

If Input the solution with b>0 ⇒   it is in the form of a +ib

The real number a equals  -3/2  and the real number b equals (√ 23)/2