Question
$$\frac{12x^2+2x-5}{2x-3} = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 12 }-\dfrac{\sqrt{ 61 }}{ 12 } & x_2 = -\dfrac{ 1 }{ 12 }+\dfrac{\sqrt{ 61 }}{ 12 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{12x^2+2x-5}{2x-3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2x-3 }. \\[1 em](2x-3)\frac{12x^2+2x-5}{2x-3} &= (2x-3)\cdot0&& \text{cancel out the denominators} \\[1 em]12x^2+2x-5 &= 0&& \\[1 em] \end{aligned} $$
$ 12x^{2}+2x-5 = 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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