As @Tomas already explained greatly in his answer you have to drive to $X_3$.
$$\frac{\partial y}{\partial X_3}= \beta_3 + 2 \times \beta_4 \times X_3$$.
As you want to now whether the derivative is positive you face the inquality:
$$0>\beta_3 + 2 \times \beta_4 \times X_3$$.
Depending on $X_3$ you can change the equation to
$$\frac{-\beta_3}{2 * \beta_4} > X_3$$
Let us look at an example in which you have real numbers for the Betas:
When you have the equation:
$\beta_1 = 5$
$\beta_2 = 3$
$\beta_3 = 4$
$\beta_4 = 2$
$y = 5 + 3X_2 + 4X_3 + 2(X_3)^2$
and $X_3$ will have a positive effect when:
$$\frac{-4}{2 \cdot 2} > X_3$$
which is simplified:
$$1 > X_3$$
library(ggplot2)
my_df <- data.frame()
ggplot(df) + xlim(-10,10) + ylim(-10,10) + geom_abline(intercept=-4, slope=4) + geom_vline(xintercept=1, colour = "red")+ xlab("X_3") + ylab("derivative of X_3")
Everything left of the red line has a positive effect on the dependent variable

Note that the "change in the conditional mean of outcome y when regressors change by one unit" is also called marginal effect. You might look at the tag description and question tagged with this tag to get a broader understanding. In your case you want to know whether the marginal effect of $X_3$ is positive (or negative).
This question: Regression with Quadratic Term - Understanding Marginal Effect is closely related to your question as it also talks about the marginal effect with a quadratic term.