Answer
The solutions are $t=-2+2i$ and $t=-2-2i$.
Work Step by Step
$ 7t^{2}+28t+56=0\qquad$ ...divide each term with $7$.
$ t^{2}+4t+8=0\qquad$ ...add $-8$ to each side.
$ t^{2}+4t+8-8=0-8\qquad$ ...simplify.
$ t^{2}+4t=-8\qquad$ ...square half the coefficient of $t$.
$(\displaystyle \frac{4}{2})^{2}=(2)^{2}=4\qquad$ ...add $4$ to each side of the expression
$ t^{2}+4t+4=-8+4\qquad$ ...simplify.
$ t^{2}+4t+4=-4\qquad$ ... write left side as a binomial squared.
$(t+2)^{2}=-4\qquad$ ...take square roots of each side.
$ t+2=\pm\sqrt{-4}\qquad$ ...simplify.($\sqrt{-4}=2i$)
$ t+2=\pm 2i\qquad$ ...add $-2$ to each side.
$ t+2-2=\pm 2i-2\qquad$ ...simplify.
$t=-2\pm 2i$
