Question
$$3 \cdot \frac{x}{2}x\cdot2+x-3+x\cdot7 = 2+x+13$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 7 }{ 6 }-\dfrac{\sqrt{ 265 }}{ 6 } & x_2 = -\dfrac{ 7 }{ 6 }+\dfrac{\sqrt{ 265 }}{ 6 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3 \cdot \frac{x}{2}x\cdot2+x-3+x\cdot7 &= 2+x+13&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]23 \cdot \frac{x}{2}x\cdot2+2x-2\cdot3+2x\cdot7 &= 2\cdot2+2x+2\cdot13&& \text{cancel out the denominators} \\[1 em]6x^2+2x-6+14x &= 4+2x+26&& \text{simplify left and right hand side} \\[1 em]6x^2+16x-6 &= 2x+30&& \text{move all terms to the left hand side } \\[1 em]6x^2+16x-6-2x-30 &= 0&& \text{simplify left side} \\[1 em]6x^2+14x-36 &= 0&& \\[1 em] \end{aligned} $$
$ 6x^{2}+14x-36 = 0 $ is a quadratic equation.
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