-x^2+96x-400=0

Solution for -x^2+96x-400=0 equation:

-x^2+96x-400=0

We add all the numbers together, and all the variables

-1x^2+96x-400=0

a = -1; b = 96; c = -400;
Δ = b2-4ac
Δ = 962-4·(-1)·(-400)
Δ = 7616
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:

$\sqrt{\Delta}=\sqrt{7616}=\sqrt{64*119}=\sqrt{64}*\sqrt{119}=8\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-8\sqrt{119}}{2*-1}=\frac{-96-8\sqrt{119}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+8\sqrt{119}}{2*-1}=\frac{-96+8\sqrt{119}}{-2}
$