Question
$$45-5x^2 = 20-\frac{x^2}{20}$$
Answer
$$ \begin{matrix}x_1 = -10 \dfrac{\sqrt{ 55 }}{ 33 } & x_2 = \dfrac{ 10 \sqrt{ 55}}{ 33 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 45-5x^2 &= 20-\frac{x^2}{20}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20\cdot45-20\cdot5x^2 &= 20\cdot20-20 \cdot \frac{x^2}{20}&& \text{cancel out the denominators} \\[1 em]900-100x^2 &= 400-x^2&& \text{simplify left and right hand side} \\[1 em]-100x^2+900 &= -x^2+400&& \text{move all terms to the left hand side } \\[1 em]-100x^2+900+x^2-400 &= 0&& \text{simplify left side} \\[1 em]-99x^2+500 &= 0&& \\[1 em] \end{aligned} $$
$ -99x^{2}+500 = 0 $ is a quadratic equation.
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