Solve for \( u \), where \( u \) is a real number. \[ \sqrt{4 u-15}+2=5 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( u=\square \)

To solve for \( u \), we start with the equation: \[ \sqrt{4u - 15} + 2 = 5 \] First, isolate the square root: \[ \sqrt{4u - 15} = 5 - 2 \] \[ \sqrt{4u - 15} = 3 \] Next, square both sides to eliminate the square root: \[ 4u - 15 = 3^2 \] \[ 4u - 15 = 9 \] Now, add 15 to both sides: \[ 4u = 9 + 15 \] \[ 4u = 24 \] Now, divide by 4: \[ u = \frac{24}{4} \] \[ u = 6 \] Now, we need to check if this solution satisfies the original equation: Substitute \( u = 6 \) back into the original equation: \[ \sqrt{4(6) - 15} + 2 = 5 \] \[ \sqrt{24 - 15} + 2 = 5 \] \[ \sqrt{9} + 2 = 5 \] \[ 3 + 2 = 5 \] This is true. Thus, the solution is: \[ u = 6 \]