2x+x(x-4)=180

Solution for 2x+x(x-4)=180 equation:

2x+x(x-4)=180

We move all terms to the left:

2x+x(x-4)-(180)=0

We multiply parentheses

x^2+2x-4x-180=0

We add all the numbers together, and all the variables

x^2-2x-180=0

a = 1; b = -2; c = -180;
Δ = b2-4ac
Δ = -22-4·1·(-180)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{181}}{2*1}=\frac{2-2\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{181}}{2*1}=\frac{2+2\sqrt{181}}{2}
$