16=2+31t+16t^2

Solution for 16=2+31t+16t^2 equation:

16=2+31t+16t^2

We move all terms to the left:

16-(2+31t+16t^2)=0

We get rid of parentheses

-16t^2-31t-2+16=0

We add all the numbers together, and all the variables

-16t^2-31t+14=0

a = -16; b = -31; c = +14;
Δ = b2-4ac
Δ = -312-4·(-16)·14
Δ = 1857
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{-(-31)-\sqrt{1857}}{2*-16}=\frac{31-\sqrt{1857}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1857}}{2*-16}=\frac{31+\sqrt{1857}}{-32}
$