Question
$$13+(13-x)x\cdot2 = 19$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 13 }{ 2 }-\dfrac{\sqrt{ 157 }}{ 2 } & x_2 = \dfrac{ 13 }{ 2 }+\dfrac{\sqrt{ 157 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 13+(13-x)x\cdot2 &= 19&& \text{simplify left side} \\[1 em]13+(13x-x^2)\cdot2 &= 19&& \\[1 em]13+26x-2x^2 &= 19&& \\[1 em]-2x^2+26x+13 &= 19&& \text{move all terms to the left hand side } \\[1 em]-2x^2+26x+13-19 &= 0&& \text{simplify left side} \\[1 em]-2x^2+26x-6 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}+26x-6 = 0 $ is a quadratic equation.
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