#### Answer

The give equation has two complex number solutions.

#### Work Step by Step

Add $2x$ and $6$ to both sides to obtain:
$$8x^2+2x+6=-2x-6+2x+6
\\8x^2+2x+6=0$$
This this equation has $a=8$, $b=2$, and $x=6$.
RECALL:
(1) The discriminant is equal to $b^2-4ac$.
(2) A quadratic equation has the following types of solutions based on the value of the discriminant:
(a) when $b^2-4ac\gt0$, the equation has two unequal rational solutions;
(b) when $b^2-4ac=0$, the equation has one, repeated rational solution; and
(c) when $b^2-4ac\lt0$, the equation has two complex number solutions;
The discriminant of the equation above is:
$$b^2-4ac = 2^2 - 4(8)(6) = 4-192=-188$$
The discriminant is negative.
Thus, the give equation has two complex number solutions.