0=-16t^2+300t+6

Solution for 0=-16t^2+300t+6 equation:

0=-16t^2+300t+6

We move all terms to the left:

0-(-16t^2+300t+6)=0

We add all the numbers together, and all the variables

-(-16t^2+300t+6)=0

We get rid of parentheses

16t^2-300t-6=0

a = 16; b = -300; c = -6;
Δ = b2-4ac
Δ = -3002-4·16·(-6)
Δ = 90384
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:

$\sqrt{\Delta}=\sqrt{90384}=\sqrt{16*5649}=\sqrt{16}*\sqrt{5649}=4\sqrt{5649}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-4\sqrt{5649}}{2*16}=\frac{300-4\sqrt{5649}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+4\sqrt{5649}}{2*16}=\frac{300+4\sqrt{5649}}{32}
$