x^2-72x+180=0

Solution for x^2-72x+180=0 equation:

x^2-72x+180=0

a = 1; b = -72; c = +180;
Δ = b2-4ac
Δ = -722-4·1·180
Δ = 4464
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:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{31}}{2*1}=\frac{72-12\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{31}}{2*1}=\frac{72+12\sqrt{31}}{2}
$