Question
$$-\frac{3}{500000}x^2+\frac{47}{2500}x+\frac{12593}{2000} = 10$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 4700 }{ 3 }-\dfrac{ 295 \sqrt{ 190}}{ 3 } & x_2 = \dfrac{ 4700 }{ 3 }+\dfrac{ 295 \sqrt{ 190}}{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -\frac{3}{500000}x^2+\frac{47}{2500}x+\frac{12593}{2000} &= 10&& \text{multiply ALL terms by } \color{blue}{ 500000 }. \\[1 em]-500000 \cdot \frac{3}{500000}x^2+500000\frac{47}{2500}x+500000\cdot\frac{12593}{2000} &= 500000\cdot10&& \text{cancel out the denominators} \\[1 em]-3x^2+9400x+3148250 &= 5000000&& \text{move all terms to the left hand side } \\[1 em]-3x^2+9400x+3148250-5000000 &= 0&& \text{simplify left side} \\[1 em]-3x^2+9400x-1851750 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+9400x-1851750 = 0 $ is a quadratic equation.
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