Projectile motion football kick problem

[Cherrybawls]

Homework Statement

A football kicker can give the ball an initial speed of 25 m/s. what are the least and greatest angles of elevation at which he can kick the ball to score a field goal from a point 50m in front of the goalposts whose horizontal bar is 3.44m above the ground?

Homework Equations

I really don't know what to do

The Attempt at a Solution

I figured I could write
V₀tcosX=50
and
V₀tsinX-.5gt²=3.44

Then I tried to find t in terms of X and got
t=50/(V₀cosX)

Then I plugged that into the other equation and I got
50tanX-12250/cos²X-2150=0

I thought then I could find the zeros and that would be my answer but it doesn't seem to be working... I can't figure out why. Maybe I totally missed the answer but either way I still need help lol. Thanks.

 

[rl.bhat]

you can write the equation of the projectile as
y = x*tanθ - (g/2*u^2)*x^2*sec^2(θ)
Put sec^2(θ) = 1 + tan^2(θ) and solve the quadratic for tanθ.

 

[Cherrybawls]

I am confused, what are you referring to with u?

 

[rl.bhat]

Sorry. u is Vo.