-16t^2+144t-224=0

Solution for -16t^2+144t-224=0 equation:

-16t^2+144t-224=0

a = -16; b = 144; c = -224;
Δ = b2-4ac
Δ = 1442-4·(-16)·(-224)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-80}{2*-16}=\frac{-224}{-32}
=+7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+80}{2*-16}=\frac{-64}{-32}
=+2
$