x^2-120x+180=0

Solution for x^2-120x+180=0 equation:

x^2-120x+180=0

a = 1; b = -120; c = +180;
Δ = b2-4ac
Δ = -1202-4·1·180
Δ = 13680
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:

$\sqrt{\Delta}=\sqrt{13680}=\sqrt{144*95}=\sqrt{144}*\sqrt{95}=12\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-12\sqrt{95}}{2*1}=\frac{120-12\sqrt{95}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+12\sqrt{95}}{2*1}=\frac{120+12\sqrt{95}}{2}
$