-16x^2-5x+200=0

Solution for -16x^2-5x+200=0 equation:

-16x^2-5x+200=0

a = -16; b = -5; c = +200;
Δ = b2-4ac
Δ = -52-4·(-16)·200
Δ = 12825
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:

$\sqrt{\Delta}=\sqrt{12825}=\sqrt{225*57}=\sqrt{225}*\sqrt{57}=15\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15\sqrt{57}}{2*-16}=\frac{5-15\sqrt{57}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15\sqrt{57}}{2*-16}=\frac{5+15\sqrt{57}}{-32}
$