Discriminant formula issue Could you please explain to me, how to get the formula of discriminant ? How can I visualize it, any articles, lectures? 
I can memorize it $b^2 - 4ac$ But, want to understand it.
Thanks. 

You must have seen a method called "completing the square" before you saw the quadratic formula in school right? This is where it comes from, in fact, if you know how to complete the square, you can derive the whole quadratic formula on your own.
Consider the quadratic equation that you're used to $$ax^2 + bx + c = 0.$$
To complete the square we need the coefficient of $x^2$ (the term in front of $x^2$, i.e. the $a$) to be $1$, so we need to divide both sides by $a$. (If $a = 0$, then the equation isn't a quadratic and we actually have $bx + c = 0$, which you can solve easily). This gives:
$$x^2 + \frac{b}{a}x + \frac{c}{a} = 0.$$
We now complete the square as usual:
$$\Bigg(x + \frac{b}{2a}\Bigg)^2 + \frac{c}{a} - \frac{b^2}{4a^2} = 0.$$
We now need to make $x$ the subject:
\begin{align}\Bigg(x + \frac{b}{2a}\Bigg)^2 &= -\Bigg(\frac{c}{a} - \frac{b^2} {4a^2}\Bigg)\\
\Bigg(x + \frac{b}{2a}\Bigg)^2 &= -\Bigg(\frac{4ac}{4a^2} - \frac{b^2} {4a^2}\Bigg)\\
\Bigg(x + \frac{b}{2a}\Bigg)^2 &= -\Bigg(\frac{4ac - b^2} {4a^2}\Bigg)\\
\Bigg(x + \frac{b}{2a}\Bigg)^2 &= \Bigg(\frac{b^2-4ac} {4a^2}\Bigg)\\
x + \frac{b}{2a} &= \pm\sqrt{ \Bigg(\frac{b^2-4ac} {4a^2} \Bigg) }\\
x + \frac{b}{2a} &= \pm\frac{\sqrt{b^2-4ac}}{2a}\\
x &= -\frac{b}{2a}\pm\frac{\sqrt{b^2-4ac}}{2a}\\
x &= \frac{-b\pm\sqrt{b^2-4ac}}{2a}.
\end{align}
Finally, the part in the square root is the discriminant.
