-16t^2+31.3987352t+6=0

Solution for -16t^2+31.3987352t+6=0 equation:

-16t^2+31.3987352t+6=0

a = -16; b = 31.3987352; c = +6;
Δ = b2-4ac
Δ = 31.39873522-4·(-16)·6
Δ = 1369.8805721597
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{-(31.3987352)-\sqrt{1369.8805721597}}{2*-16}=\frac{-31.3987352-\sqrt{1369.8805721597}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31.3987352)+\sqrt{1369.8805721597}}{2*-16}=\frac{-31.3987352+\sqrt{1369.8805721597}}{-32}
$