0=-16t^2+114

Solution for 0=-16t^2+114 equation:

0=-16t^2+114

We move all terms to the left:

0-(-16t^2+114)=0

We add all the numbers together, and all the variables

-(-16t^2+114)=0

We get rid of parentheses

16t^2-114=0

a = 16; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·16·(-114)
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{114}}{2*16}=\frac{0-8\sqrt{114}}{32}
=-\frac{8\sqrt{114}}{32}
=-\frac{\sqrt{114}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{114}}{2*16}=\frac{0+8\sqrt{114}}{32}
=\frac{8\sqrt{114}}{32}
=\frac{\sqrt{114}}{4}
$