x^2-120x+1800=0

Solution for x^2-120x+1800=0 equation:

x^2-120x+1800=0

a = 1; b = -120; c = +1800;
Δ = b2-4ac
Δ = -1202-4·1·1800
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-60\sqrt{2}}{2*1}=\frac{120-60\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+60\sqrt{2}}{2*1}=\frac{120+60\sqrt{2}}{2}
$