Y=-16t^2+700

Solution for Y=-16t^2+700 equation:

=-16Y^2+700

We move all terms to the left:

-(-16Y^2+700)=0

We get rid of parentheses

16Y^2-700=0

a = 16; b = 0; c = -700;
Δ = b2-4ac
Δ = 02-4·16·(-700)
Δ = 44800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44800}=\sqrt{6400*7}=\sqrt{6400}*\sqrt{7}=80\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{7}}{2*16}=\frac{0-80\sqrt{7}}{32}
=-\frac{80\sqrt{7}}{32}
=-\frac{5\sqrt{7}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{7}}{2*16}=\frac{0+80\sqrt{7}}{32}
=\frac{80\sqrt{7}}{32}
=\frac{5\sqrt{7}}{2}
$