8+40.8t-16t^2=2

Solution for 8+40.8t-16t^2=2 equation:

8+40.8t-16t^2=2

We move all terms to the left:

8+40.8t-16t^2-(2)=0

We add all the numbers together, and all the variables

-16t^2+40.8t+6=0

a = -16; b = 40.8; c = +6;
Δ = b2-4ac
Δ = 40.82-4·(-16)·6
Δ = 2048.64
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{-(40.8)-\sqrt{2048.64}}{2*-16}=\frac{-40.8-\sqrt{2048.64}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40.8)+\sqrt{2048.64}}{2*-16}=\frac{-40.8+\sqrt{2048.64}}{-32}
$