2=72t-16t^2

Solution for 2=72t-16t^2 equation:

2=72t-16t^2

We move all terms to the left:

2-(72t-16t^2)=0

We get rid of parentheses

16t^2-72t+2=0

a = 16; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·16·2
Δ = 5056
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:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{79}}{2*16}=\frac{72-8\sqrt{79}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{79}}{2*16}=\frac{72+8\sqrt{79}}{32}
$