-16t^2-76t+2=0

Solution for -16t^2-76t+2=0 equation:

-16t^2-76t+2=0

a = -16; b = -76; c = +2;
Δ = b2-4ac
Δ = -762-4·(-16)·2
Δ = 5904
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:

$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-12\sqrt{41}}{2*-16}=\frac{76-12\sqrt{41}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+12\sqrt{41}}{2*-16}=\frac{76+12\sqrt{41}}{-32}
$