Question
$$\frac{1+x}{2}+\frac{3-x}{4} = 3x^2$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 24 }-\dfrac{\sqrt{ 241 }}{ 24 } & x_2 = \dfrac{ 1 }{ 24 }+\dfrac{\sqrt{ 241 }}{ 24 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= 3x^2&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4\cdot3x^2&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 12x^2&& \text{simplify left side} \\[1 em]x+5 &= 12x^2&& \text{move all terms to the left hand side } \\[1 em]x+5-12x^2 &= 0&& \text{simplify left side} \\[1 em]-12x^2+x+5 &= 0&& \\[1 em] \end{aligned} $$
$ -12x^{2}+x+5 = 0 $ is a quadratic equation.
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