Question
$$(\frac{16}{9})^2x^2+x^2 = 48^2$$
Answer
$$ \begin{matrix}x_1 = 24 & x_2 = -24 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (\frac{16}{9})^2x^2+x^2 &= 48^2&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9(\frac{16}{9})^2x^2+9x^2 &= 9\cdot48^2&& \text{cancel out the denominators} \\[1 em]27x^2+9x^2 &= 20736&& \text{simplify left side} \\[1 em]36x^2 &= 20736&& \text{move all terms to the left hand side } \\[1 em]36x^2-20736 &= 0&& \\[1 em] \end{aligned} $$
$ 36x^{2}-20736 = 0 $ is a quadratic equation.
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