I'm looking forward to finding the roots in $x$ of the following function:
$$\frac{C^2}{\gamma}\arcsin\left(\frac{\gamma(x\sqrt{\beta}+(B-x)\sqrt{\alpha})}{C^2}\right)=x\sqrt{\alpha}-(x+B)\sqrt{\beta}-2(T-C)B$$
Where $C,\gamma,T$ and $C$ are constants and $\alpha$ and $\beta$ are functions of $x$ given by $\alpha=C^2-\gamma^2x^2$ and $\beta=C^2-\gamma^2(B-x)^2$. Despite a large number of constants, does anyone have a hint of how I can proceed to find the roots of this function? I already know that depending on the constant values it has a real root for $x$. I'll be pleased with any kind of help :)