$$(x-1)^2-(2x-1)^2 = 9-x$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 11 }}{ 2 }i & x_2 = \dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 11 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x-1)^2-(2x-1)^2 &= 9-x&& \text{simplify left and right hand side} \\[1 em]x^2-2x+1-(4x^2-4x+1) &= -x+9&& \\[1 em]x^2-2x+1-4x^2+4x-1 &= -x+9&& \\[1 em]x^2-2x+1-4x^2+4x-1 &= -x+9&& \\[1 em]-3x^2+2x &= -x+9&& \text{move all terms to the left hand side } \\[1 em]-3x^2+2x+x-9 &= 0&& \text{simplify left side} \\[1 em]-3x^2+3x-9 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+3x-9 = 0 $ is a quadratic equation.
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