Solve the following equation:

$$
4 x^{2}+\sqrt{x^{2}-3.5 x+2}=14 x+10
$$
Our equation can also be written as:

$$
4 x^{2}-14 x-10=-\sqrt{x^{2}-3.5 x+2}
$$

or, if $x^{2}-3.5 x=y$, then

$$
4 y-10=-\sqrt{y+2}
$$

from which $y_{1}=2$ and $y_{2}=\frac{49}{16}$, and thus

$$
x_{1}=4, x_{2}=-\frac{1}{2}, x_{3}=\frac{7}{4}(1+\sqrt{2}), x_{4}=\frac{7}{4}(1-\sqrt{2})
$$

(Kornél Miklóssy, Arad.)

The problem was also solved by: Dévai E., Fekete M., Friedländer H., Füstös P., Heimlich P., Jánosy Gy., Kepes I., Kiss J., Lázár B., Meleghy Gy., Pichler S., Rajz E., Schön M., Schuster Gy., Steiger J., Tóth B., Wáhl V., Wottitz R.