$$x-\frac{4x+3}{x+5} = \frac{2x+27}{x+5}$$
Answer
$$ \begin{matrix}x_1 = -5 & x_2 = 6 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x-\frac{4x+3}{x+5} &= \frac{2x+27}{x+5}&& \text{multiply ALL terms by } \color{blue}{ x+5 }. \\[1 em](x+5)x-(x+5)\frac{4x+3}{x+5} &= (x+5)\frac{2x+27}{x+5}&& \text{cancel out the denominators} \\[1 em]x^2+5x-(4x+3) &= 2x+27&& \text{simplify left side} \\[1 em]x^2+5x-4x-3 &= 2x+27&& \\[1 em]x^2+x-3 &= 2x+27&& \text{move all terms to the left hand side } \\[1 em]x^2+x-3-2x-27 &= 0&& \text{simplify left side} \\[1 em]x^2-x-30 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-x-30 = 0 $ is a quadratic equation.
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