Finding the initial velocity using quadratic

[Rammer24]

Homework Statement

I need to find Vi, knowing the following:

Δt=6/Vi cos40

Viy=Vi sin40

Δy=4m

ay=-g = -9.8m/s^2

Homework Equations

Quadratic: x= [-b +/- √(b^2-4ac)]/2a

Kinematic equation to be used: Δy=ViyΔt + 1/2ayΔt^2

The Attempt at a Solution

Δy=ViyΔt + 1/2ayΔt^2

4=(Vi sin40)(6/Vi cos40) -4.9(6/Vi cos40)^2

This is where I'm stuck, I don't know how to continue the problem and solve for Vi.

EDIT: I solved for Vi and got and answer of 9.9m/s, but according to my teacher, the correct answer should be 17.05m/s, so I'm definitely making a mistake somewhere in the algebra.

Thanks

 

[Kurdt]

IF you show your working it will be easy to see where you're going wrong.