$$4x = -5x^2+1$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = \dfrac{ 1 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4x &= -5x^2+1&& \text{move all terms to the left hand side } \\[1 em]4x+5x^2-1 &= 0&& \text{simplify left side} \\[1 em]5x^2+4x-1 &= 0&& \\[1 em] \end{aligned} $$
$ 5x^{2}+4x-1 = 0 $ is a quadratic equation.
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