To solve the quadratic equation \( 6u^2 - 54u - 132 = 0 \), we can start by simplifying the equation.
First, divide every term by 6:
\[ u^2 - 9u - 22 = 0 \]
Next, we can apply the quadratic formula \( u = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1, b = -9, c = -22 \).
Calculating the discriminant:
\[ b^2 - 4ac = (-9)^2 - 4 \cdot 1 \cdot (-22) = 81 + 88 = 169 \]
Now, substitute \( b \), the square root of the discriminant, and \( a \) into the quadratic formula:
\[ u = \frac{-(-9) \pm \sqrt{169}}{2 \cdot 1} = \frac{9 \pm 13}{2} \]
This gives us two solutions:
- For \( u = \frac{9 + 13}{2} \):
\[ u = \frac{22}{2} = 11 \]
- For \( u = \frac{9 - 13}{2} \):
\[ u = \frac{-4}{2} = -2 \]
Thus, the solutions to the equation \( 6u^2 - 54u - 132 = 0 \) are
\[ u = 11, -2 \]
The final answer is:
\[ \boxed{11, -2} \]