To solve the quadratic equation \(x^2 + 5x - 36 = 0\), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Where \(a = 1\), \(b = 5\), and \(c = -36\).
First, we calculate the discriminant \(b^2 - 4ac\):
\[ b^2 - 4ac = 5^2 - 4 \cdot 1 \cdot (-36) = 25 + 144 = 169 \]
Now, we can apply the quadratic formula:
\[ x = \frac{-5 \pm \sqrt{169}}{2 \cdot 1} \] \[ x = \frac{-5 \pm 13}{2} \]
This gives us two potential solutions:
- \(x = \frac{-5 + 13}{2} = \frac{8}{2} = 4\)
- \(x = \frac{-5 - 13}{2} = \frac{-18}{2} = -9\)
Since we are looking for the positive solution, the answer is:
\[ \boxed{4} \]