$2x + 3 = \frac{34}{x - 5}$
(2x + 3)(x − 5) = 34
$2x^2 + 3x - 10x - 15 - 34 = 0$
$2x^2 - 7x - 49 = 0$
D = 49 + 2 * 4 * 49 = 49 + 392 = 441
$x = \frac{7 ± \sqrt{441}}{4}$
$x_1 = \frac{7 - 21}{4} = \frac{-14}{4} = -3,5$
$x_2 = \frac{7 + 21}{4} = \frac{28}{4} = 7$
при x = −3,5:
y = 2x + 3 = 2 * (−3,5) + 3 = −7 + 3 = −4;
при x = 7:
y = 2x + 3 = 2 * 7 + 3 = 14 + 3 = 17.
Ответ: две точки пересечения графиков функций (−3,5;−4) и (7;17).

$2x = \frac{x^2 - 5x}{x + 3}$
$2x(x + 3) = x^2 - 5x$
$2x^2 + 6x = x^2 - 5x$
$x^2 + 11x = 0$
x(x + 11) = 0
$x_1 = 0$
$x_2 = -11$
при x = 0:
y = 2x = 2 * 0 = 0;
при x = −11:
y = 2x = 2 * (−11) = −22.
Ответ: две точки пересечения графиков функций (0;0) и (−11;−22).