Answer:
[tex]x_{1=} \frac{-1+i\sqrt{35} }{6} \\\\x_{2=} \frac{-1-i\sqrt{35} }{6}[/tex]
Step-by-step explanation:
Using the quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]
We will have two solutions:
[tex]x_{1}\\ x_{2}[/tex]
-3x^2-x-3=0 a=-3 b=-1 c=-3
We have:
[tex]x_{1}=\frac{1+\sqrt{-35} }{-6}\\\\x_{2}=\frac{1-\sqrt{-35} }{-6}\\[/tex]
we can write:
[tex]x_{1}=\frac{-1+\sqrt{-35} }{6}\\\\x_{2}=\frac{-1-\sqrt{-35} }{6}\\[/tex]
The solutions are not real numbers.
So, we know: [tex]i=\sqrt{-1}[/tex]
Finally we have:
[tex]x_{1}=\frac{-1+i\sqrt{35} }{6}\\\\x_{2}=\frac{-1-i\sqrt{35} }{6}\\[/tex]
