Answer
The solutions are $-4+3\sqrt{2}$ and $-4-3\sqrt{2}$.
Work Step by Step
$ 6x(x+8)=12\qquad$ ... use the Distributive Property.
$ 6x^{2}+48x=12\qquad$ ...divide each term with $6$.
$ x^{2}+8x=2\qquad$ ...square half the coefficient of $x$.
$(\displaystyle \frac{8}{2})^{2}=4^{2}=16\qquad$ ...add $16$ to each side of the expression
$ x^{2}+8x+16=2+16\qquad$ ... write left side as a binomial squared.
$(x+4)^{2}=2+16\qquad$ ...simplify.
$(x+4)^{2}=18\qquad$ ...take square roots of each side.
$ x+4=\pm\sqrt{18}\qquad$ ...add $-4$ to each side of the expression
$ x+4-4=\pm\sqrt{18}-4\qquad$ ...simplify.
$ x=-4\pm\sqrt{18}\qquad$ ...rewrite $\sqrt{18}$ as $\sqrt{9\cdot 2.}$
$ x=-4\pm\sqrt{9\cdot 2}\qquad$ ...evaluate $\sqrt{9}$.
$x=-4\pm 3\sqrt{2}$
