#### Answer

$x=-1\pm\frac{2\sqrt{15}}{5}$

#### Work Step by Step

We complete the square:
$5x^{2}+10x-7=0$
$x^{2}+2x-\frac{7}{5}=0$
$x^{2}+2x=\frac{7}{5}$
$x^{2}+2x+1=\frac{7}{5}+1=\frac{12}{5}$
$(x+1)^{2}=\frac{12}{5}$
$x+1=\pm\sqrt{\frac{12}{5}}=\pm\sqrt{\frac{4*3*5}{5*5}}=\pm\frac{2\sqrt{15}}{5}$
$x=-1\pm\frac{2\sqrt{15}}{5}$