2x+x(x+20)=180

Solution for 2x+x(x+20)=180 equation:

2x+x(x+20)=180

We move all terms to the left:

2x+x(x+20)-(180)=0

We multiply parentheses

x^2+2x+20x-180=0

We add all the numbers together, and all the variables

x^2+22x-180=0

a = 1; b = 22; c = -180;
Δ = b2-4ac
Δ = 222-4·1·(-180)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{301}}{2*1}=\frac{-22-2\sqrt{301}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{301}}{2*1}=\frac{-22+2\sqrt{301}}{2}
$