31=16t^2+50t+4

Solution for 31=16t^2+50t+4 equation:

31=16t^2+50t+4

We move all terms to the left:

31-(16t^2+50t+4)=0

We get rid of parentheses

-16t^2-50t-4+31=0

We add all the numbers together, and all the variables

-16t^2-50t+27=0

a = -16; b = -50; c = +27;
Δ = b2-4ac
Δ = -502-4·(-16)·27
Δ = 4228
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:

$\sqrt{\Delta}=\sqrt{4228}=\sqrt{4*1057}=\sqrt{4}*\sqrt{1057}=2\sqrt{1057}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1057}}{2*-16}=\frac{50-2\sqrt{1057}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1057}}{2*-16}=\frac{50+2\sqrt{1057}}{-32}
$