I'm programming a game where I need projectiles to hit moving targets. I was able to make my projectile hit accurately a stationary target using a formula I found on Wikipedia about projectile trajectories.
Now, I couldn't figure out how to hit a moving target. So I stumbled upon his question: Trajectory of a projectile meets a moving object (2D)
I would be very happy to understand how could I solve this equation in order to get the theta value. I was never good at mathematics, and unfortunely, learning math by myself has been very hard. So, could anybody explain me the required steps to end with something like $θ = (...)$. The equation of the matter is the following: $$gx^2+2(v\cosθ+u\cosϕ)(vy\cosθ+uy\cosϕ−vx\sinθ+ux\sinϕ)=0$$
Thanks in advance. (if anything is not correct, please inform me, first post :))
Introducting intermediate constants, your equation has the form
$$(a\cos\theta+b)(c\cos\theta+d\sin\theta+e)+f=A\cos^2\theta+B\sin\theta\cos\theta+C\cos\theta+D\sin\theta+E=0,$$ not very "solution friendly".
We can rationalize it by means of the transform
$$\cos\theta=\frac{u^2-1}{u^2+1},\sin\theta=\frac{2u}{u^2+1}$$ and this yields a quartic
$$A(u^2-1)^2+2Bu(u^2-1)+C(u^4-1)+2Du(u^2+1)+E(u^2+1)^2=0.$$
There are closed formulas, but they can be painful to use, probably better to use a numerical solver.