<s>[INST] This is equation is giving me issues $x^2 - 6x + 15 = 0 $ I was given this equation $x^2 - 6x + 15 = 0 $
I tried to look for numbers whose sum is big and product of ac and i could not find any. I tried using the quadratic formula
$$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
 and this is what i got
$x = \frac{6\pm\sqrt{-24}}{2}$
I just dont know what to do from here: any help would be appreacited.
 [/INST] So you need to find the roots as follow:
Note that:
$$ i^2 = -1$$
$$ x = \frac{6\pm \sqrt{-24}}{2}=\frac{6\pm i\sqrt{24}}{2} $$
$$ x= \frac{6\pm 2i\sqrt{6}}{2} = 3\pm i\sqrt{6}$$
Further explanation ($i^2 = -1$):
let $a = \sqrt{-24}$
$a^2 = -24= 24 \times -1= 24i^2$
$a =\pm \sqrt{24} \times \sqrt{i^2}= \pm i\sqrt{24} = \pm i \times \sqrt{4} \times \sqrt{6} = \pm2i\sqrt{6}$
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