I'm given the function and must work out the x coordinate on f(x), A, which a line dividing the area between the function and the x-axis from [0,2] into 2 parts of equal area passes through. The area total area between the function and x-axis from [0,2] is 4 square units.

I've got it down to

I'm kinda stuck there. Is there another way to do it that doesn't require me to solve polynomial equations?