t=-16t^2+16t+192

Solution for t=-16t^2+16t+192 equation:

t=-16t^2+16t+192

We move all terms to the left:

t-(-16t^2+16t+192)=0

We get rid of parentheses

16t^2-16t+t-192=0

We add all the numbers together, and all the variables

16t^2-15t-192=0

a = 16; b = -15; c = -192;
Δ = b2-4ac
Δ = -152-4·16·(-192)
Δ = 12513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{12513}}{2*16}=\frac{15-\sqrt{12513}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{12513}}{2*16}=\frac{15+\sqrt{12513}}{32}
$