Question
$$3x^2 = 81-x^2$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 9 }{ 2 } & x_2 = -\dfrac{ 9 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3x^2 &= 81-x^2&& \text{simplify right side} \\[1 em]3x^2 &= -x^2+81&& \text{move all terms to the left hand side } \\[1 em]3x^2+x^2-81 &= 0&& \text{simplify left side} \\[1 em]4x^2-81 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}-81 = 0 $ is a quadratic equation.
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