How to separate Quadratic formula between delta and x' and x''?

Question

New on Tex, LaTex. Hoping this is not a difficult question:

This is the LaTex for the quadratic equation formula:

$$\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array}$$

How to I separate this between Delta and X in a way I have also x', x''?

Edit: This a visual approach of what I am looking for:

Thanks

Answer 1

For the Delta and X there is no need for any particular alignment, so I think gather is what you want here. Whereas for x' and x'' you want align. Also, for big fractions you want to display, use dfrac (from amsmath), and for some short bits of text between equations, use shortintertext from mathtools).

\documentclass{article}
\usepackage{amsmath,mathtools}
\begin{document}
For a quadratic with determinant $ \Delta $ where
\begin{gather}
\Delta = b^2 - 4ac, \\
\shortintertext{we have the general solution}
x = \dfrac{-b \pm \sqrt{\Delta}}{2a}.
\end{gather}
This has the two roots $ x' $ and $ x'' $ given by
\begin{align}
x'  & = \dfrac{-b + \sqrt{\Delta}}{2a} \\
\shortintertext{and}
x'' & = \dfrac{-b - \sqrt{\Delta}}{2a}. 
\end{align}
\end{document}

As an aside, consider using x^+ and x^- instead of the prime notation, as it makes things clearer, as people will think you're talking about derivatives.

Answer 2

I hope that this is ok:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\begin{document}
[\begin{matrix}
\Delta =b^2-4ac\
     x = \dfrac{- b\pm\sqrt{b^2- 4ac}}{2a}\[.5em]
     x' = \dfrac{- b+\sqrt{b^2- 4ac}}{2a}\[.5em]
     x'' = \dfrac{- b-\sqrt{b^2- 4ac}}{2a}
\end{matrix}]
\end{document}

Using the \cdot:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\begin{document}
[\begin{matrix}
\Delta =b^2-4\cdot a\cdot c\
     x = \dfrac{- b\pm\sqrt{b^2- 4ac}}{2\cdot a}\[.5em]
     x' = \dfrac{- b+\sqrt{b^2- 4ac}}{2\cdot a}\[.5em]
     x'' = \dfrac{- b-\sqrt{b^2- 4ac}}{2\cdot a}
\end{matrix}]
\end{document}