How Can You Simplify Calculations for Artillery Projectile Motion?

[Philosophaie]

Given:
A fixed barrel velocity, $$v_{0}$$
An elevation of the piece of artilery, e
Target distance, x
Target elevation, te

Find:
time of travel, t
angle of the artilery, a

Equations:
$$y_{0}$$ = te - e

x = $$v_{0}$$ * cos(a) * t
y = $$y_{0}$$ + $$v_{0}$$ * sin(a) * t - 0.5 * g * $$t^{2}$$

If you try solving these for a and t, it gets ugly. Is there an equation I am missing or another way around this?

 

[Cyosis]

You're y_0 seems wrong. At t=0 the elevation should be e should it not? Other than that it looks good, two equations, two variables therefore solvable.

tip:put your entire equations between tex brackets it will look at a lot better.