Find the value of $x$ if the area of the rectangle is 78 with the dimensions x+7 and x

Step 1 ：Let's find the value of $x$ if the area of the rectangle is 78 with the dimensions $x+7$ and $x$.

Step 2 ：The area of a rectangle is given by the product of its length and width. In this case, the length is $x+7$ and the width is $x$. So, we can set up the equation $(x+7)*x = 78$ to find the value of $x$.

Step 3 ：Solving this equation gives us two solutions: $x = -13$ and $x = 6$. However, since $x$ represents a dimension, it cannot be negative. Therefore, the only valid solution is $x = 6$.

Step 4 ：Final Answer: The value of $x$ is \(\boxed{6}\).