$$20 = \frac{1}{2}(x+3)+(x+5)x$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 11 }{ 4 }-\dfrac{\sqrt{ 417 }}{ 4 } & x_2 = -\dfrac{ 11 }{ 4 }+\dfrac{\sqrt{ 417 }}{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 20 &= \frac{1}{2}(x+3)+(x+5)x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot20 &= 2 \cdot \frac{1}{2}(x+3)+2(x+5)x&& \text{cancel out the denominators} \\[1 em]40 &= x+3+2x^2+10x&& \text{simplify right side} \\[1 em]40 &= 2x^2+11x+3&& \text{move all terms to the left hand side } \\[1 em]40-2x^2-11x-3 &= 0&& \text{simplify left side} \\[1 em]-2x^2-11x+37 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}-11x+37 = 0 $ is a quadratic equation.
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