>
> > sage: solve(-(1/2*sqrt((4*w+1)+1))*t+w==0,w) 
> > [w == 1/2*sqrt(4*w + 2)*t] 
>
> Well, if I'm not mistaken, Sage punts to Maxima's 'solve' function, 
> which, I'm sorry to report, is not very strong (it can solve a 
> relatively narrow range of problems). But I find that Maxima's 
> 'to_poly_solve' can solve it. Maybe someone here can say how to 
> call it from Sage. 
>
> In principle

var('w,t')
solve(-(1/2*sqrt((4*w+1)+1))*t+w==0,w,to_poly_solve='force') 

or 

var('w,t')
solve(-(1/2*sqrt((4*w+1)+1))*t+w==0,w,to_poly_solve=True) 
 
should work to call that, but for some reason they don't.

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