Can this be converted into a polynomial equation for $x$? I came upon this monster equation while fiddling with the area of pentagons:
$$\sqrt{(a+b+c-x)(a+b-c+x)(a+c-b+x)(b+c-a+x)}+\sqrt{(c+d+x)(c+d-x)(c-d+x)(d-c+x)}=4T$$ 
Where $a,b,c,d,e,T$ are known quantities. So my question is:


*

*Can this be converted into a polynomial equation for $x$?

*If so how can we do it, and what would be its degree?


Any help is appreciated :)

If you have an equation of the form $\sqrt a + \sqrt b = c$ then by taking squares we get $2\sqrt {ab} = c^2-a-b$, and then $4ab = (c^2-a-b)^2$.
You can also develop the product in the equation $(\sqrt a + \sqrt b - c)(\sqrt a - \sqrt b - c)(- \sqrt a + \sqrt b - c)(- \sqrt a - \sqrt b - c) = 0$, which gives you (again) $4ab = (c^2-a-b)^2$.
