Generated by the Physics Derivation Graph. Eq. \ref{eq:8882098} is an initial equation. $$ax^2 + bx + c = 0 \label{eq:8882098}$$ Divide both sides of Eq. \ref{eq:8882098} by $$a$$; yields Eq. \ref{eq:7777621}. $$x^2 + (b/a)x+(c/a) = 0 \label{eq:7777621}$$ Subtract $$c/a$$ from both sides of Eq. \ref{eq:7777621}; yields Eq. \ref{eq:1212129}. $$x^2 + (b/a)x = -c/a \label{eq:1212129}$$ Add $$(b/(2 a))^2$$ to both sides of Eq. \ref{eq:1212129}; yields Eq. \ref{eq:1120000}. $$x^2 + (b/a)x + (b/(2 a))^2 = -c/a + (b/(2 a))^2 \label{eq:1120000}$$ Change variable $$h$$ to $$b/(2 a)$$ in Eq. \ref{eq:9091270}; yields Eq. \ref{eq:1239010}. $$x^2 + 2 x (b/(2 a)) + (b/(2 a))^2 = (x + (b/(2 a)))^2 \label{eq:1239010}$$ Simplify Eq. \ref{eq:1239010}; yields Eq. \ref{eq:1734000}. $$x^2 + x(b/a) + (b/(2 a))^2 = (x+(b/(2 a)))^2 \label{eq:1734000}$$ Eq. \ref{eq:9091270} is an initial equation. $$x^2 + 2 x h + h^2 = (x + h)^2 \label{eq:9091270}$$ LHS of Eq. \ref{eq:1120000} is equal to LHS of Eq. \ref{eq:1734000}; yields Eq. \ref{eq:2985412}. $$(x+(b/(2 a)))^2 = -(c/a) + (b/(2 a))^2 \label{eq:2985412}$$ Take the square root of both sides of Eq. \ref{eq:2985412}; yields Eq. \ref{eq:6608123} and Eq. \ref{eq:6608102}. $$x+(b/(2 a)) = -\sqrt{(b/(2 a))^2 - (c/a)} \label{eq:6608123}$$ $$x+(b/(2 a)) = \sqrt{(b/(2 a))^2 - (c/a)} \label{eq:6608102}$$ Subtract $$b/(2 a)$$ from both sides of Eq. \ref{eq:6608123}; yields Eq. \ref{eq:4433112}. $$x = \sqrt{(b/(2 a))^2 - (c/a)}-(b/(2 a)) \label{eq:4433112}$$ Subtract $$b/(2 a)$$ from both sides of Eq. \ref{eq:6608102}; yields Eq. \ref{eq:2657355}. $$x = -\sqrt{(b/(2 a))^2 - (c/a)}-(b/(2 a)) \label{eq:2657355}$$ Simplify Eq. \ref{eq:2657355}; yields Eq. \ref{eq:8811221}. $$x = \frac{-b-\sqrt{b^2-4ac}}{2 a} \label{eq:8811221}$$ Simplify Eq. \ref{eq:4433112}; yields Eq. \ref{eq:8761200}. $$x = \frac{-b+\sqrt{b^2-4ac}}{2 a} \label{eq:8761200}$$ Eq. \ref{eq:8811221} is one of the final equations. Eq. \ref{eq:8761200} is one of the final equations.