2x(x+20)+x=180

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

2x(x+20)+x=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2+x+40x-180=0

We add all the numbers together, and all the variables

2x^2+41x-180=0

a = 2; b = 41; c = -180;
Δ = b2-4ac
Δ = 412-4·2·(-180)
Δ = 3121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-\sqrt{3121}}{2*2}=\frac{-41-\sqrt{3121}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{3121}}{2*2}=\frac{-41+\sqrt{3121}}{4}
$