72=-16t^2+64t+112

Solution for 72=-16t^2+64t+112 equation:

72=-16t^2+64t+112

We move all terms to the left:

72-(-16t^2+64t+112)=0

We get rid of parentheses

16t^2-64t-112+72=0

We add all the numbers together, and all the variables

16t^2-64t-40=0

a = 16; b = -64; c = -40;
Δ = b2-4ac
Δ = -642-4·16·(-40)
Δ = 6656
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:

$\sqrt{\Delta}=\sqrt{6656}=\sqrt{256*26}=\sqrt{256}*\sqrt{26}=16\sqrt{26}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{26}}{2*16}=\frac{64-16\sqrt{26}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{26}}{2*16}=\frac{64+16\sqrt{26}}{32}
$