Solve the equation using the quadratic formula. \[ r^{2}+3 r-1=0 \]

Step 1 ：The given equation is a quadratic equation in the form of \(ax^2 + bx + c = 0\). The quadratic formula to solve this equation is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 2 ：Here, \(a = 1\), \(b = 3\), and \(c = -1\). We can substitute these values into the quadratic formula to find the roots of the equation.

Step 3 ：Calculate the discriminant, \(D = b^2 - 4ac = 13\).

Step 4 ：Substitute the values of a, b, and D into the quadratic formula to find the roots of the equation. The roots are \(r1 = 0.30277563773199456\) and \(r2 = -3.302775637731995\).

Step 5 ：Final Answer: The roots of the equation \(r^{2}+3 r-1=0\) are \(\boxed{0.30277563773199456}\) and \(\boxed{-3.302775637731995}\).