So, a is acceleration, F is a force Vo is Vsubscript0 (V_{0}) and you want to solve for something unspecified, is this correct?
Your notation is confusing  do you mean boldface to be a vector? In which case, how can you have a scalar equal a vector? Shouldn't acceleration also be a vector?
If all these can be taken in the x direction ... ditching the boldface:[tex]ma = V_0\frac{a^2}{a^2+x^2}[/tex]... perhaps you want to find x as a function of time?
Then why not rearrange so all the powers of "a" are on the left and all the others are on the right, substitute a=d²x/dt² and solve the differential equation?
Don't you get a quadratic in "a"?
