-16t^2-30t+8=0

Solution for -16t^2-30t+8=0 equation:

-16t^2-30t+8=0

a = -16; b = -30; c = +8;
Δ = b2-4ac
Δ = -302-4·(-16)·8
Δ = 1412
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:

$\sqrt{\Delta}=\sqrt{1412}=\sqrt{4*353}=\sqrt{4}*\sqrt{353}=2\sqrt{353}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{353}}{2*-16}=\frac{30-2\sqrt{353}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{353}}{2*-16}=\frac{30+2\sqrt{353}}{-32}
$