-x2+48x-512=0

Solution for -x2+48x-512=0 equation:

-x2+48x-512=0

We add all the numbers together, and all the variables

-1x^2+48x-512=0

a = -1; b = 48; c = -512;
Δ = b2-4ac
Δ = 482-4·(-1)·(-512)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16}{2*-1}=\frac{-64}{-2}
=+32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16}{2*-1}=\frac{-32}{-2}
=+16
$