Question
$$x+1-x^2 = 2(2x^2-1)$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 10 }-\dfrac{\sqrt{ 61 }}{ 10 } & x_2 = \dfrac{ 1 }{ 10 }+\dfrac{\sqrt{ 61 }}{ 10 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+1-x^2 &= 2(2x^2-1)&& \text{simplify left and right hand side} \\[1 em]-x^2+x+1 &= 4x^2-2&& \text{move all terms to the left hand side } \\[1 em]-x^2+x+1-4x^2+2 &= 0&& \text{simplify left side} \\[1 em]-5x^2+x+3 &= 0&& \\[1 em] \end{aligned} $$
$ -5x^{2}+x+3 = 0 $ is a quadratic equation.
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