Question
$$\frac{4}{5}(2x+5)-5x(x-1)+\frac{2}{5}x = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 7 }{ 10 }-\dfrac{\sqrt{ 129 }}{ 10 } & x_2 = \dfrac{ 7 }{ 10 }+\dfrac{\sqrt{ 129 }}{ 10 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{5}(2x+5)-5x(x-1)+\frac{2}{5}x &= 0&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{4}{5}(2x+5)-55x(x-1)+5\frac{2}{5}x &= 5\cdot0&& \text{cancel out the denominators} \\[1 em]8x+20-(25x^2-25x)+2x &= 0&& \text{simplify left side} \\[1 em]8x+20-25x^2+25x+2x &= 0&& \\[1 em]-25x^2+35x+20 &= 0&& \\[1 em] \end{aligned} $$
$ -25x^{2}+35x+20 = 0 $ is a quadratic equation.
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