9=-16t^2+16t+96

Solution for 9=-16t^2+16t+96 equation:

9=-16t^2+16t+96

We move all terms to the left:

9-(-16t^2+16t+96)=0

We get rid of parentheses

16t^2-16t-96+9=0

We add all the numbers together, and all the variables

16t^2-16t-87=0

a = 16; b = -16; c = -87;
Δ = b2-4ac
Δ = -162-4·16·(-87)
Δ = 5824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5824}=\sqrt{64*91}=\sqrt{64}*\sqrt{91}=8\sqrt{91}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{91}}{2*16}=\frac{16-8\sqrt{91}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{91}}{2*16}=\frac{16+8\sqrt{91}}{32}
$