Question
$$6(x-1)^2 = 53$$
Answer
$$ \begin{matrix}x_1 = 1-\dfrac{\sqrt{ 318 }}{ 6 } & x_2 = 1+\dfrac{\sqrt{ 318 }}{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 6(x-1)^2 &= 53&& \text{simplify left side} \\[1 em]6(x^2-2x+1) &= 53&& \\[1 em]6x^2-12x+6 &= 53&& \text{move all terms to the left hand side } \\[1 em]6x^2-12x+6-53 &= 0&& \text{simplify left side} \\[1 em]6x^2-12x-47 &= 0&& \\[1 em] \end{aligned} $$
$ 6x^{2}-12x-47 = 0 $ is a quadratic equation.
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