$$3z^2+5z+1 = 3$$
Answer
$$ \begin{matrix}z_1 = \dfrac{ 1 }{ 3 } & z_2 = -2 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3z^2+5z+1 &= 3&& \text{move all terms to the left hand side } \\[1 em]3z^2+5z+1-3 &= 0&& \text{simplify left side} \\[1 em]3z^2+5z-2 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+5x-2 = 0 $ is a quadratic equation.
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