Answer
$\frac{-2h\pm\sqrt{4h^{2}+2A}}{2}$
Work Step by Step
$A=2x^{2}+4xh$
$2x^{2}+4hx-A=0$
We use the quadratic formula:
$x=\frac{-(4h)\pm\sqrt{(4h)^{2}-4(2)(-A)}}{2(2)}=\frac{-4h\pm\sqrt{16h^{2}+8A}}{4}=\frac{-4h\pm\sqrt{4(4h^{2}+2A)}}{4}=\frac{-4h\pm 2\sqrt{4h^{2}+2A}}{4}=\frac{-2h\pm\sqrt{4h^{2}+2A}}{2}$