-x^2+48x-180=0

Solution for -x^2+48x-180=0 equation:

-x^2+48x-180=0

We add all the numbers together, and all the variables

-1x^2+48x-180=0

a = -1; b = 48; c = -180;
Δ = b2-4ac
Δ = 482-4·(-1)·(-180)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{11}}{2*-1}=\frac{-48-12\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{11}}{2*-1}=\frac{-48+12\sqrt{11}}{-2}
$