<s>[INST] Quadratic formula does not work If I put the equation: $5x^2-x-4 =0$  in the quadratic formula, than I get 
$x = 1$ or $x = \frac{-4}{5}$
but the real zeros are: $x = -1$ or $x = \frac{4}{5}$
Can somebody explain me if the quadratic formula fails or me?
 [/INST] The quadratic formula comes from "completing the square". Let's do that to your examples:
\begin{eqnarray*}
5x^2-x-4 &=& 0 \\ \\
x^2 - \tfrac{1}{5}x - \tfrac{4}{5} &=& 0 \\ \\
x^2 - \tfrac{1}{5}x &=& \tfrac{4}{5} \\ \\
\left(x - \tfrac{1}{10}\right)^{2} - \tfrac{1}{100} &=& \tfrac{4}{5} \\ \\
\left(x - \tfrac{1}{10}\right)^{2} &=& \tfrac{4}{5} + \tfrac{1}{100} \\ \\
\left(x - \tfrac{1}{10}\right)^{2} &=& \tfrac{81}{100} \\ \\
x - \tfrac{1}{10} &=& \pm \tfrac{9}{10} \\ \\
x &=& \tfrac{1}{10} \pm \tfrac{9}{10} \\ \\
x&=& -\tfrac{4}{5} \ \ \text{or} \ \ 1
\end{eqnarray*}
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