x(x+13)+(x+20)=180

Solution for x(x+13)+(x+20)=180 equation:

x(x+13)+(x+20)=180

We move all terms to the left:

x(x+13)+(x+20)-(180)=0

We multiply parentheses

x^2+13x+(x+20)-180=0

We get rid of parentheses

x^2+13x+x+20-180=0

We add all the numbers together, and all the variables

x^2+14x-160=0

a = 1; b = 14; c = -160;
Δ = b2-4ac
Δ = 142-4·1·(-160)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{209}}{2*1}=\frac{-14-2\sqrt{209}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{209}}{2*1}=\frac{-14+2\sqrt{209}}{2}
$