Solve for \( u \), where \( u \) is a real number. \( \quad \sqrt{11 u-30}=u \) If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

To solve the equation \( \sqrt{11u - 30} = u \), we start by squaring both sides to eliminate the square root: \[ 11u - 30 = u^2. \] Rearranging gives us: \[ u^2 - 11u + 30 = 0. \] This is a quadratic equation, which we can solve using factoring or the quadratic formula. Let's try factoring first: We need two numbers that multiply to \( 30 \) and add up to \( -11 \). The numbers \( -6 \) and \( -5 \) fit this criteria. So, we can factor the equation as: \[ (u - 6)(u - 5) = 0. \] Setting each factor to zero gives us the potential solutions: \[ u - 6 = 0 \quad \Rightarrow \quad u = 6, \] \[ u - 5 = 0 \quad \Rightarrow \quad u = 5. \] Next, we should check both solutions to ensure they satisfy the original equation: For \( u = 6 \): \[ \sqrt{11(6) - 30} = \sqrt{66 - 30} = \sqrt{36} = 6, \] which is valid. For \( u = 5 \): \[ \sqrt{11(5) - 30} = \sqrt{55 - 30} = \sqrt{25} = 5, \] which is also valid. Both solutions work, so the final answer is: \( u = 6, 5 \)