144=-16t^2+94t+256

Solution for 144=-16t^2+94t+256 equation:

144=-16t^2+94t+256

We move all terms to the left:

144-(-16t^2+94t+256)=0

We get rid of parentheses

16t^2-94t-256+144=0

We add all the numbers together, and all the variables

16t^2-94t-112=0

a = 16; b = -94; c = -112;
Δ = b2-4ac
Δ = -942-4·16·(-112)
Δ = 16004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16004}=\sqrt{4*4001}=\sqrt{4}*\sqrt{4001}=2\sqrt{4001}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-94)-2\sqrt{4001}}{2*16}=\frac{94-2\sqrt{4001}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-94)+2\sqrt{4001}}{2*16}=\frac{94+2\sqrt{4001}}{32}
$