x^2-180x+1800=0

Solution for x^2-180x+1800=0 equation:

x^2-180x+1800=0

a = 1; b = -180; c = +1800;
Δ = b2-4ac
Δ = -1802-4·1·1800
Δ = 25200
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:

$\sqrt{\Delta}=\sqrt{25200}=\sqrt{3600*7}=\sqrt{3600}*\sqrt{7}=60\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-60\sqrt{7}}{2*1}=\frac{180-60\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+60\sqrt{7}}{2*1}=\frac{180+60\sqrt{7}}{2}
$