Answer:
[tex]x=\frac{-2\pm \sqrt{11}i }{3}[/tex]
Step-by-step explanation:
The given equation is
[tex]3x^2+4x=-5[/tex]
We rewrite in the general quadratic equation form to get,
[tex]3x^2+4x+5=0[/tex]
By comparing to [tex]ax^2+bx+c=0[/tex], we have
[tex]a=3,b=4,c=5[/tex]
We can solve using the quadratic formula, which is given by
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
We substitute the values to obtain;
[tex]x=\frac{-4\pm \sqrt{4^2-4(3)(5)} }{2(3)}[/tex]
[tex]x=\frac{-4\pm \sqrt{16-60} }{6}[/tex]
[tex]x=\frac{-4\pm \sqrt{-44} }{6}[/tex]
[tex]x=\frac{-4\pm 2\sqrt{11}i }{6}[/tex]
[tex]x=\frac{-2\pm \sqrt{11}i }{3}[/tex]
The correct answer is A.
