16t^2-8t-30=0

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

16t^2-8t-30=0

a = 16; b = -8; c = -30;
Δ = b2-4ac
Δ = -82-4·16·(-30)
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{31}}{2*16}=\frac{8-8\sqrt{31}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{31}}{2*16}=\frac{8+8\sqrt{31}}{32}
$