x(x-6)=180

Solution for x(x-6)=180 equation:

x(x-6)=180

We move all terms to the left:

x(x-6)-(180)=0

We multiply parentheses

x^2-6x-180=0

a = 1; b = -6; c = -180;
Δ = b2-4ac
Δ = -62-4·1·(-180)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{21}}{2*1}=\frac{6-6\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{21}}{2*1}=\frac{6+6\sqrt{21}}{2}
$