$$\frac{3}{2}y^2+\frac{11}{10}y+1 = 0$$
Answer
$$ \begin{matrix}y_1 = -\dfrac{ 11 }{ 30 }+\dfrac{\sqrt{ 479 }}{ 30 }i & y_2 = -\dfrac{ 11 }{ 30 }-\dfrac{\sqrt{ 479 }}{ 30 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{2}y^2+\frac{11}{10}y+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{3}{2}y^2+10\frac{11}{10}y+10\cdot1 &= 10\cdot0&& \text{cancel out the denominators} \\[1 em]15y^2+11y+10 &= 0&& \\[1 em] \end{aligned} $$
$ 15x^{2}+11x+10 = 0 $ is a quadratic equation.
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