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

Solution for -16t^2+31t-2=0 equation:

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

a = -16; b = 31; c = -2;
Δ = b2-4ac
Δ = 312-4·(-16)·(-2)
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-7\sqrt{17}}{2*-16}=\frac{-31-7\sqrt{17}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+7\sqrt{17}}{2*-16}=\frac{-31+7\sqrt{17}}{-32}
$