#### Answer

The solutions are $2$ and $6$

#### Work Step by Step

$ 7(x-4)^{2}-18=10\qquad$ ...add $18$ to each side.
$ 7(x-4)^{2}-18+18=10+18\qquad$ ...simplify.
$ 7(x-4)^{2}=28\qquad$ ...divide each side with $7$.
$(x-4)^{2}=4\qquad$ ...take square roots of each side.
$\sqrt{(x-4)^{2}}=\sqrt{4}\qquad$ ...simplify.
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$(x-4)=\pm\sqrt{4}\qquad$ ...evaluate $\sqrt{4} $ ($\sqrt{4}=2$)
$ x-4=\pm 2\qquad$ ...add $4$ to each side.
$ x-4+4=\pm 2+4\qquad$ ...simplify.
$x=4\pm 2$