To solve the 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:
\[ b^2 - 4ac = 5^2 - 4(1)(-36) = 25 + 144 = 169 \]
Now we can plug this value into the quadratic formula:
\[ x = \frac{-5 \pm \sqrt{169}}{2 \cdot 1} = \frac{-5 \pm 13}{2} \]
This yields 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:
\[ \boxed{4} \]