16t^2-320t+1538=0

Solution for 16t^2-320t+1538=0 equation:

16t^2-320t+1538=0

a = 16; b = -320; c = +1538;
Δ = b2-4ac
Δ = -3202-4·16·1538
Δ = 3968
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:

$\sqrt{\Delta}=\sqrt{3968}=\sqrt{64*62}=\sqrt{64}*\sqrt{62}=8\sqrt{62}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-8\sqrt{62}}{2*16}=\frac{320-8\sqrt{62}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+8\sqrt{62}}{2*16}=\frac{320+8\sqrt{62}}{32}
$