Solution of Quadratic

Clear[x];
Solve[a (x^2)+2b x+c==0,x]

xp=((-b+(Sqrt[(b^2)-a c]))/a)

xpalt=(c/(-b-(Sqrt[(b^2)-a c])))

Simplify[{xp,xpalt}]

Simplify[xp-xpalt]

LogLogPlot[{-xp,-xpalt}/.{a->1,c->1},{b,(10^7),(10^9)}]