456=900-16t^2

Solution for 456=900-16t^2 equation:

456=900-16t^2

We move all terms to the left:

456-(900-16t^2)=0

We get rid of parentheses

16t^2-900+456=0

We add all the numbers together, and all the variables

16t^2-444=0

a = 16; b = 0; c = -444;
Δ = b2-4ac
Δ = 02-4·16·(-444)
Δ = 28416
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:

$\sqrt{\Delta}=\sqrt{28416}=\sqrt{256*111}=\sqrt{256}*\sqrt{111}=16\sqrt{111}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{111}}{2*16}=\frac{0-16\sqrt{111}}{32}
=-\frac{16\sqrt{111}}{32}
=-\frac{\sqrt{111}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{111}}{2*16}=\frac{0+16\sqrt{111}}{32}
=\frac{16\sqrt{111}}{32}
=\frac{\sqrt{111}}{2}
$