x(x+54)+180=0

Solution for x(x+54)+180=0 equation:

x(x+54)+180=0

We multiply parentheses

x^2+54x+180=0

a = 1; b = 54; c = +180;
Δ = b2-4ac
Δ = 542-4·1·180
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{61}}{2*1}=\frac{-54-6\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{61}}{2*1}=\frac{-54+6\sqrt{61}}{2}
$