To solve the quadratic equation \( x^2 + 5x - 36 = 0 \), we can use the quadratic formula, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, the coefficients are:
- \( a = 1 \)
- \( b = 5 \)
- \( c = -36 \)
First, we calculate the discriminant \( b^2 - 4ac \):
\[ b^2 - 4ac = 5^2 - 4 \cdot 1 \cdot (-36) = 25 + 144 = 169 \]
Now, we apply the quadratic formula:
\[ x = \frac{-5 \pm \sqrt{169}}{2 \cdot 1} = \frac{-5 \pm 13}{2} \]
This results in two possible solutions:
- Using the positive root:
\[ x = \frac{-5 + 13}{2} = \frac{8}{2} = 4 \]
- Using the negative root:
\[ x = \frac{-5 - 13}{2} = \frac{-18}{2} = -9 \]
Since we are looking for the positive solution, the answer is:
\[ \boxed{4} \]