  In this paper, we prove that for any K\"ahler metrics $\omega_0$ and $\chi$
on $M$, there exists
$\omega_\varphi=\omega_0+\sqrt{-1}\partial\bar\partial\varphi>0$ satisfying the
J-equation $\mathrm{tr}_{\omega_\varphi}\chi=c$ if and only if
$(M,[\omega_0],[\chi])$ is uniformly J-stable. As a corollary, we can find many
constant scalar curvature K\"ahler metrics with $c_1<0$. Using the same method,
we also prove a similar result for the deformed Hermitian-Yang-Mills equation
when the angle is in $(\frac{n\pi}{2}-\frac{\pi}{4},\frac{n\pi}{2})$.
