8=-16t^2+261

Solution for 8=-16t^2+261 equation:

8=-16t^2+261

We move all terms to the left:

8-(-16t^2+261)=0

We get rid of parentheses

16t^2-261+8=0

We add all the numbers together, and all the variables

16t^2-253=0

a = 16; b = 0; c = -253;
Δ = b2-4ac
Δ = 02-4·16·(-253)
Δ = 16192
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:

$\sqrt{\Delta}=\sqrt{16192}=\sqrt{64*253}=\sqrt{64}*\sqrt{253}=8\sqrt{253}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{253}}{2*16}=\frac{0-8\sqrt{253}}{32}
=-\frac{8\sqrt{253}}{32}
=-\frac{\sqrt{253}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{253}}{2*16}=\frac{0+8\sqrt{253}}{32}
=\frac{8\sqrt{253}}{32}
=\frac{\sqrt{253}}{4}
$