16t^2-120t-2=0

Solution for 16t^2-120t-2=0 equation:

16t^2-120t-2=0

a = 16; b = -120; c = -2;
Δ = b2-4ac
Δ = -1202-4·16·(-2)
Δ = 14528
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:

$\sqrt{\Delta}=\sqrt{14528}=\sqrt{64*227}=\sqrt{64}*\sqrt{227}=8\sqrt{227}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{227}}{2*16}=\frac{120-8\sqrt{227}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{227}}{2*16}=\frac{120+8\sqrt{227}}{32}
$