$x^{2}+6 x-5=0$

Step 1 ：Solve the quadratic equation $x^{2}+6 x-5=0$ using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a=1$, $b=6$, and $c=-5$.

Step 2 ：Calculate the discriminant: $\Delta = b^2 - 4ac = 6^2 - 4(1)(-5) = 36 + 20 = 56$.

Step 3 ：Find the two solutions: $x_1 = \frac{-6 + \sqrt{56}}{2(1)} \approx 0.74$ and $x_2 = \frac{-6 - \sqrt{56}}{2(1)} \approx -6.74$.

Step 4 ：Final Answer: The solutions to the equation are $x \approx \boxed{0.74}$ and $x \approx \boxed{-6.74}$.