Answer:
[tex]\frac{5+i\sqrt{3}}{2}}[/tex]
Step-by-step explanation:
I assume you want the roots. Here we go:
Use the quadratic formula: [tex]\frac{-(-30) plus or minus \sqrt{(-30)^2-4(6)(42)} }{2\cdot6}[/tex].
The discriminant is 900 - 1008, or -108 (so we will need i, the complex number that means [tex]\sqrt{-1}[/tex]).
This means on the top you get 30 + 6isqrt3 and on the bottom you get 12.
So the fraction is [tex]\frac{30+6i\sqrt{3}}{12}=\boxed{\frac{5+i\sqrt{3}}{2}}.\blacksquare[/tex]
Note: This is just one of the roots, I am sure you can find the second one!
