Distinct real roots

Characteristic equation.
$$r^2 + 3r - 4 = 0.$$
The discriminant is $\Delta = 9 + 16 = 25$, so the roots are
$$r_1 = \frac{-3+5}{2} = 1, \qquad r_2 = \frac{-3-5}{2} = -4.$$

General solution.
$$y(x) = Ae^x + Be^{-4x}, \qquad A,B \in \mathbb{R}.$$