224=144t+-16t2

Solution for 224=144t+-16t2 equation:

224=144t+-16t^2

We move all terms to the left:

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

We use the square of the difference formula

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

We get rid of parentheses

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