x(x-30)=180

Solution for x(x-30)=180 equation:

x(x-30)=180

We move all terms to the left:

x(x-30)-(180)=0

We multiply parentheses

x^2-30x-180=0

a = 1; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·1·(-180)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{5}}{2*1}=\frac{30-18\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{5}}{2*1}=\frac{30+18\sqrt{5}}{2}
$