$$2x^2-7 = \frac{107}{2}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 11 }{ 2 } & x_2 = -\dfrac{ 11 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x^2-7 &= \frac{107}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot2x^2-2\cdot7 &= 2\cdot\frac{107}{2}&& \text{cancel out the denominators} \\[1 em]4x^2-14 &= 107&& \text{move all terms to the left hand side } \\[1 em]4x^2-14-107 &= 0&& \text{simplify left side} \\[1 em]4x^2-121 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}-121 = 0 $ is a quadratic equation.
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