The goal is to calculate the area of the quadrangle. The length of the sides are given, and we know that 2EB=ED (E is the intesection of AC and BD, it isn't on the picture, sorry).
I named the area of BEC t, and the area ABD T, I figured out that CED=2t and AED=2T. I used the t=absin(x)/2 formula to calculate the area of ABC and ACD, ACD is twice the area of ABC, and with that I got the ratio of sin(Beta) and sin(Delta).
I also used the fact that sin^2(x)=1-cos^2(x) to calculate that cos^2(Delta)=(64cos^2(x)+225)/289.
I then used the cosine rule on side AC with both triangles, then I used the value of cos^2(Delta) to get that cos(Beta)=2.5, which is nonsense. Where did it go wrong?