Solve the equation:
$$
36 x^{4}-84 x^{3}+37 x^{2}+14 x-3=0 \text {. }
$$
$$
\begin{array}{l}
\text { Sol } \because \Delta=b^{3}+43(2 n d-6 c) \\
=(-84)^{3}+4 \times 36(2 \times 36 \\
\times: 4-(-84) \times 37 \text { J } \\
=0 \text {, } \\
\end{array}
$$
$\therefore$ The equation can be transformed into
$$
\left(x^{2}+\frac{b}{2 a} x\right)^{2}+\frac{4 a c-b^{2}}{4 a^{2}} \cdot\left(x^{2}+\frac{b}{2 a} x\right)+\frac{e}{a}=1 j \text {, }
$$

which is $\left(x^{2}-\frac{7}{6} x\right)^{2}-\frac{1}{3}\left(x^{2}-\frac{7}{6} x\right)-\frac{1}{12}=0$,
$$
\begin{array}{l}
\left(6 x^{2}-7 x\right)^{2}-2\left(6 x^{2}-7 x\right)-3=0, \\
\left(6 x^{2}-7 x-3\right)\left(6 x^{2}-7 x+1\right)=0 .
\end{array}
$$

Solving, we get $x_{1}=-\frac{1}{3}, x_{2}=\frac{3}{2}, x_{3}=1$,
$$
x_{4}=\frac{1}{6} .
$$