-x^2+36x-96=0

Solution for -x^2+36x-96=0 equation:

-x^2+36x-96=0

We add all the numbers together, and all the variables

-1x^2+36x-96=0

a = -1; b = 36; c = -96;
Δ = b2-4ac
Δ = 362-4·(-1)·(-96)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{57}}{2*-1}=\frac{-36-4\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{57}}{2*-1}=\frac{-36+4\sqrt{57}}{-2}
$