Question
$$4x^2+3x+1 = 7x^2+2x-3$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = \dfrac{ 4 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4x^2+3x+1 &= 7x^2+2x-3&& \text{move all terms to the left hand side } \\[1 em]4x^2+3x+1-7x^2-2x+3 &= 0&& \text{simplify left side} \\[1 em]-3x^2+x+4 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+x+4 = 0 $ is a quadratic equation.
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