-16t2+80t+224=0

Solution for -16t2+80t+224=0 equation:

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

a = -16; b = 80; c = +224;
Δ = b2-4ac
Δ = 802-4·(-16)·224
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-144}{2*-16}=\frac{-224}{-32}
=+7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+144}{2*-16}=\frac{64}{-32}
=-2
$