$$4x\cdot2+8x+15+x\cdot2-x-27-(x+5)(x-7) = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 19 }{ 2 }-\dfrac{\sqrt{ 453 }}{ 2 } & x_2 = \dfrac{ 19 }{ 2 }+\dfrac{\sqrt{ 453 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4x\cdot2+8x+15+x\cdot2-x-27-(x+5)(x-7) &= 0&& \text{simplify left side} \\[1 em]8x+8x+15+x-27-(x+5)(x-7) &= 0&& \\[1 em]16x+15+x-27-(x+5)(x-7) &= 0&& \\[1 em]17x-12-(x+5)(x-7) &= 0&& \\[1 em]17x-12-(x^2-7x+5x-35) &= 0&& \\[1 em]17x-12-(x^2-2x-35) &= 0&& \\[1 em]17x-12-x^2+2x+35 &= 0&& \\[1 em]-x^2+19x+23 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+19x+23 = 0 $ is a quadratic equation.
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