x=-16x^2+208x-200

Solution for x=-16x^2+208x-200 equation:

x=-16x^2+208x-200

We move all terms to the left:

x-(-16x^2+208x-200)=0

We get rid of parentheses

16x^2-208x+x+200=0

We add all the numbers together, and all the variables

16x^2-207x+200=0

a = 16; b = -207; c = +200;
Δ = b2-4ac
Δ = -2072-4·16·200
Δ = 30049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-207)-\sqrt{30049}}{2*16}=\frac{207-\sqrt{30049}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-207)+\sqrt{30049}}{2*16}=\frac{207+\sqrt{30049}}{32}
$