72=4t+16t^2

Solution for 72=4t+16t^2 equation:

72=4t+16t^2

We move all terms to the left:

72-(4t+16t^2)=0

We get rid of parentheses

-16t^2-4t+72=0

a = -16; b = -4; c = +72;
Δ = b2-4ac
Δ = -42-4·(-16)·72
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-68}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+68}{2*-16}=\frac{72}{-32}
=-2+1/4
$