Question
$$2x^2+3 = \frac{3}{2}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{\sqrt{ 3 }}{ 2 } i & x_2 = - \dfrac{\sqrt{ 3 }}{ 2 } i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x^2+3 &= \frac{3}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot2x^2+2\cdot3 &= 2\cdot\frac{3}{2}&& \text{cancel out the denominators} \\[1 em]4x^2+6 &= 3&& \text{move all terms to the left hand side } \\[1 em]4x^2+6-3 &= 0&& \text{simplify left side} \\[1 em]4x^2+3 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+3 = 0 $ is a quadratic equation.
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