16t^2-100t-40=0

Solution for 16t^2-100t-40=0 equation:

16t^2-100t-40=0

a = 16; b = -100; c = -40;
Δ = b2-4ac
Δ = -1002-4·16·(-40)
Δ = 12560
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:

$\sqrt{\Delta}=\sqrt{12560}=\sqrt{16*785}=\sqrt{16}*\sqrt{785}=4\sqrt{785}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{785}}{2*16}=\frac{100-4\sqrt{785}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{785}}{2*16}=\frac{100+4\sqrt{785}}{32}
$