$$\frac{4x^2-2x+1}{2x+3} = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 4 }+\dfrac{\sqrt{ 3 }}{ 4 }i & x_2 = \dfrac{ 1 }{ 4 }-\dfrac{\sqrt{ 3 }}{ 4 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4x^2-2x+1}{2x+3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2x+3 }. \\[1 em](2x+3)\frac{4x^2-2x+1}{2x+3} &= (2x+3)\cdot0&& \text{cancel out the denominators} \\[1 em]4x^2-2x+1 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}-2x+1 = 0 $ is a quadratic equation.
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