-16x^2+200=0

Solution for -16x^2+200=0 equation:

-16x^2+200=0

a = -16; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-16)·200
Δ = 12800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12800}=\sqrt{6400*2}=\sqrt{6400}*\sqrt{2}=80\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{2}}{2*-16}=\frac{0-80\sqrt{2}}{-32}
=-\frac{80\sqrt{2}}{-32}
=-\frac{5\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{2}}{2*-16}=\frac{0+80\sqrt{2}}{-32}
=\frac{80\sqrt{2}}{-32}
=\frac{5\sqrt{2}}{-2}
$