222. Find the relationship between the coefficients of the equation $a x^{2}+b x+c=0$, if the sum of its roots is twice their difference.
Let $x_{1}, x_{2}$ be the roots of the given equation. Then $x_{1}+x_{2}=-\frac{b}{a} ; x_{1} \cdot x_{2}=\frac{c}{a}$. According to the problem,

$$
x_{1}+x_{2}=2\left(x_{1}-x_{2}\right)
$$

from which $x_{1}=3 x_{2}$. If $x_{1}=3 x_{2}$, then

$$
x_{1}+x_{2}=4 x_{2}=-\frac{b}{a} ; \quad x_{1} x_{2}=3 x_{2}^{2}=\frac{c}{a}
$$

from which $\frac{3 b^{2}}{16 a^{2}}=\frac{c}{a}$ or $3 b^{2}=16 a c$ - the required condition.