5=-16t^2+311

Solution for 5=-16t^2+311 equation:

5=-16t^2+311

We move all terms to the left:

5-(-16t^2+311)=0

We get rid of parentheses

16t^2-311+5=0

We add all the numbers together, and all the variables

16t^2-306=0

a = 16; b = 0; c = -306;
Δ = b2-4ac
Δ = 02-4·16·(-306)
Δ = 19584
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:

$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{34}}{2*16}=\frac{0-24\sqrt{34}}{32}
=-\frac{24\sqrt{34}}{32}
=-\frac{3\sqrt{34}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{34}}{2*16}=\frac{0+24\sqrt{34}}{32}
=\frac{24\sqrt{34}}{32}
=\frac{3\sqrt{34}}{4}
$