Question
$$16x^2+9x^2 = \frac{47}{10}$$
Answer
$$ \begin{matrix}x_1 = - \dfrac{\sqrt{ 470 }}{ 50 } & x_2 = \dfrac{\sqrt{ 470 }}{ 50 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 16x^2+9x^2 &= \frac{47}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot16x^2+10\cdot9x^2 &= 10\cdot\frac{47}{10}&& \text{cancel out the denominators} \\[1 em]160x^2+90x^2 &= 47&& \text{simplify left side} \\[1 em]250x^2 &= 47&& \text{move all terms to the left hand side } \\[1 em]250x^2-47 &= 0&& \\[1 em] \end{aligned} $$
$ 250x^{2}-47 = 0 $ is a quadratic equation.
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