$$\frac{1+x}{2}+\frac{3-x}{4} = -648x^2+153x-9$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 611 }{ 5184 }+\dfrac{\sqrt{ 51767 }}{ 5184 }i & x_2 = \dfrac{ 611 }{ 5184 }-\dfrac{\sqrt{ 51767 }}{ 5184 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= -648x^2+153x-9&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= -4\cdot648x^2+4\cdot153x-4\cdot9&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= -2592x^2+612x-36&& \text{simplify left side} \\[1 em]x+5 &= -2592x^2+612x-36&& \text{move all terms to the left hand side } \\[1 em]x+5+2592x^2-612x+36 &= 0&& \text{simplify left side} \\[1 em]2592x^2-611x+41 &= 0&& \\[1 em] \end{aligned} $$
$ 2592x^{2}-611x+41 = 0 $ is a quadratic equation.
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