Question
$$x(x+7)+5 = (2x-1)^2$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 3 } & x_2 = 4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x(x+7)+5 &= (2x-1)^2&& \text{simplify left and right hand side} \\[1 em]x^2+7x+5 &= 4x^2-4x+1&& \text{move all terms to the left hand side } \\[1 em]x^2+7x+5-4x^2+4x-1 &= 0&& \text{simplify left side} \\[1 em]-3x^2+11x+4 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+11x+4 = 0 $ is a quadratic equation.
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