$$3x^2-7 = 27^2x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 243 }{ 2 }-\dfrac{ 5 \sqrt{ 21261}}{ 6 } & x_2 = \dfrac{ 243 }{ 2 }+\dfrac{ 5 \sqrt{ 21261}}{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3x^2-7 &= 27^2x&& \text{simplify right side} \\[1 em]3x^2-7 &= 729x&& \text{move all terms to the left hand side } \\[1 em]3x^2-7-729x &= 0&& \text{simplify left side} \\[1 em]3x^2-729x-7 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}-729x-7 = 0 $ is a quadratic equation.
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