3000=(16t^2)+440

Solution for 3000=(16t^2)+440 equation:

3000=(16t^2)+440

We move all terms to the left:

3000-((16t^2)+440)=0

We get rid of parentheses

-16t^2-440+3000=0

We add all the numbers together, and all the variables

-16t^2+2560=0

a = -16; b = 0; c = +2560;
Δ = b2-4ac
Δ = 02-4·(-16)·2560
Δ = 163840
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:

$\sqrt{\Delta}=\sqrt{163840}=\sqrt{16384*10}=\sqrt{16384}*\sqrt{10}=128\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128\sqrt{10}}{2*-16}=\frac{0-128\sqrt{10}}{-32}
=-\frac{128\sqrt{10}}{-32}
=-\frac{4\sqrt{10}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128\sqrt{10}}{2*-16}=\frac{0+128\sqrt{10}}{-32}
=\frac{128\sqrt{10}}{-32}
=\frac{4\sqrt{10}}{-1}
$