numerical solution of a transcendental equation I need some help with a program in MATHEMATICA or MAPPLE, that solves the following transcendental equation: $$\alpha+2x+2\sqrt{\beta+\alpha x+x^{2}}=e^{-t\frac{2}{\alpha}}(\alpha+2\sqrt{\beta})e^{{\frac{2}{\alpha}} (\sqrt{\beta+a(\alpha+a)}-\sqrt{\beta})}$$. Can someone, please, help me with this issue? P.S: How can I use this numerical solution, if I need a formula for $x(t)$ to use it further on in calculating some other physical quantities? For instance, I need to calculate pressure=$\frac{1}{x(t)^{6}}$ amd for this I need the expression of $x(t)$.

You do not really need a computer program to solve this equation. In reality you have an equation of the type \begin{equation} \alpha + 2x + 2 \sqrt{\beta + \alpha x + x^2} = f(\alpha, \beta, a, t) =: f. \end{equation} You convert into something more manageable by noticing that this equation implies \begin{equation} \left( 2 \sqrt{\beta + \alpha x + x^2} \right)^2 = 4 \left( \beta + \alpha x + x^2 \right) = (f - \alpha - 2 x)^2 \end{equation} which you can easily convert to a second degree equation in $x$. Take care and insert your solution in the original equation.