-4x^2+200=0

Solution for -4x^2+200=0 equation:

-4x^2+200=0

a = -4; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-4)·200
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*-4}=\frac{0-40\sqrt{2}}{-8}
=-\frac{40\sqrt{2}}{-8}
=-\frac{5\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*-4}=\frac{0+40\sqrt{2}}{-8}
=\frac{40\sqrt{2}}{-8}
=\frac{5\sqrt{2}}{-1}
$