x(x-72)=180

Solution for x(x-72)=180 equation:

x(x-72)=180

We move all terms to the left:

x(x-72)-(180)=0

We multiply parentheses

x^2-72x-180=0

a = 1; b = -72; c = -180;
Δ = b2-4ac
Δ = -722-4·1·(-180)
Δ = 5904
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:

$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{41}}{2*1}=\frac{72-12\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{41}}{2*1}=\frac{72+12\sqrt{41}}{2}
$