Answer
The solutions are $x=-7+\sqrt{41}$ and $x=-7-\sqrt{41}$.
Work Step by Step
$ 3x^{2}+42x=-24\qquad$ ...divide each side with $3$.
$ x^{2}+14x=-8\qquad$ ...square half the coefficient of $x$.
$(\displaystyle \frac{14}{2})^{2}=(7)^{2}=49\qquad$ ...add $49$ to each side of the expression
$ x^{2}+14x+49=-8+49\qquad$ ...simplify.
$ x^{2}+14x+49=41\qquad$ ... write left side as a binomial squared.
$(x+7)^{2}=41\qquad$ ...take square roots of each side.
$ x+7=\pm\sqrt{41}\qquad$ ...add $-7$ to each side.
$ x+7-7=\pm\sqrt{41}-7\qquad$ ...simplify.
$x=-7\pm\sqrt{41}$
