Wyprowadzenie delty
(1)
\begin{equation} ax^2+bx+c=0 \end{equation}
(2)
\begin{align} x^2+\frac{b}{a}x+\frac{c}{a}=0 \end{align}
(3)
\begin{align} x^2+\frac{b}{a}x+\frac{b^2}{4a^2}-\frac{b^2}{4a^2}+\frac{c}{a}=0 \end{align}
(4)
\begin{align} \left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a^2}+\frac{c}{a}=0 \end{align}
(5)
\begin{align} \left(x+\frac{b}{2a}\right)^2-\frac{b^2}{4a^2}+\frac{4ac}{4a^2}=0 \end{align}
(6)
\begin{align} \left(x+\frac{b}{2a}\right)^2-\frac{b^2-4ac}{4a^2}=0 \end{align}
(7)
\begin{align} \left(x+\frac{b}{2a}\right)^2-\frac{\Delta}{4a^2}=0 \end{align}
(8)
\begin{align} \left(x+\frac{b}{2a}\right)^2-\left(\frac{\sqrt{\Delta}}{2a}\right)^2=0 \end{align}
(9)
\begin{align} \left(x+\frac{b-\sqrt{\Delta}}{2a}\right)\left(x+\frac{b+\sqrt{\Delta}}{2a}\right)=0 \end{align}
(10)
\begin{align} x=\frac{-b+\sqrt{\Delta}}{2a} \vee x=\frac{-b-\sqrt{\Delta}}{2a} \end{align}
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