-x^2+180x-5400=0

Solution for -x^2+180x-5400=0 equation:

-x^2+180x-5400=0

We add all the numbers together, and all the variables

-1x^2+180x-5400=0

a = -1; b = 180; c = -5400;
Δ = b2-4ac
Δ = 1802-4·(-1)·(-5400)
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-60\sqrt{3}}{2*-1}=\frac{-180-60\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+60\sqrt{3}}{2*-1}=\frac{-180+60\sqrt{3}}{-2}
$