Answer
$x=-4\pm\frac{3\sqrt{6}}{2}$
Work Step by Step
We complete the square:
$2x^{2}+16x+5=0$
$x^{2}+8x+\frac{5}{2}=0$
$x^{2}+8x=-\frac{5}{2}$
$x^{2}+8x+16=-\frac{5}{2}+16=\frac{27}{2}$
$(x+4)^{2}=\frac{27}{2}$
$x+4=\displaystyle \pm\sqrt{\frac{27}{2}}=\pm\sqrt{\frac{9*3*2}{2*2}}=\pm\frac{3\sqrt{6}}{2}$
$x=-4\pm\frac{3\sqrt{6}}{2}$
