Step 1 :Given the quadratic equation \(x^{2}+4 x-5=0\)
Step 2 :Identify the coefficients as \(a = 1\), \(b = 4\), and \(c = -5\)
Step 3 :Calculate the discriminant \(D = b^2 - 4ac = 36\)
Step 4 :Use the quadratic formula to find the solutions for x: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Step 5 :Substitute the values into the formula to get \(x_1 = -5.0\) and \(x_2 = 1.0\)
Step 6 :Final Answer: The solutions to the equation are \(\boxed{x_{1}=-5, x_{2}=1}\)