Question
$$x^2-5x-\frac{15}{4} = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 5 }{ 2 }-\sqrt{ 10 } & x_2 = \dfrac{ 5 }{ 2 }+\sqrt{ 10 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2-5x-\frac{15}{4} &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4x^2-4\cdot5x-4\cdot\frac{15}{4} &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]4x^2-20x-15 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}-20x-15 = 0 $ is a quadratic equation.
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