$$\frac{1}{2}x^2-2x+\frac{65}{32} = 0$$
Answer
$$ \begin{matrix}x_1 = 2+\dfrac{ 1 }{ 4 }i & x_2 = 2-\dfrac{ 1 }{ 4 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{2}x^2-2x+\frac{65}{32} &= 0&& \text{multiply ALL terms by } \color{blue}{ 32 }. \\[1 em]32 \cdot \frac{1}{2}x^2-32\cdot2x+32\cdot\frac{65}{32} &= 32\cdot0&& \text{cancel out the denominators} \\[1 em]16x^2-64x+65 &= 0&& \\[1 em] \end{aligned} $$
$ 16x^{2}-64x+65 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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