308=-16t^2+80t+224

Solution for 308=-16t^2+80t+224 equation:

308=-16t^2+80t+224

We move all terms to the left:

308-(-16t^2+80t+224)=0

We get rid of parentheses

16t^2-80t-224+308=0

We add all the numbers together, and all the variables

16t^2-80t+84=0

a = 16; b = -80; c = +84;
Δ = b2-4ac
Δ = -802-4·16·84
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-32}{2*16}=\frac{48}{32}
=1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+32}{2*16}=\frac{112}{32}
=3+1/2
$