$$\frac{2x^2+3x-1}{x-4} = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 3 }{ 4 }-\dfrac{\sqrt{ 17 }}{ 4 } & x_2 = -\dfrac{ 3 }{ 4 }+\dfrac{\sqrt{ 17 }}{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2x^2+3x-1}{x-4} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-4 }. \\[1 em](x-4)\frac{2x^2+3x-1}{x-4} &= (x-4)\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2+3x-1 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+3x-1 = 0 $ is a quadratic equation.
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