x+2x(x+40)=180

Solution for x+2x(x+40)=180 equation:

x+2x(x+40)=180

We move all terms to the left:

x+2x(x+40)-(180)=0

We multiply parentheses

2x^2+x+80x-180=0

We add all the numbers together, and all the variables

2x^2+81x-180=0

a = 2; b = 81; c = -180;
Δ = b2-4ac
Δ = 812-4·2·(-180)
Δ = 8001
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:

$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-3\sqrt{889}}{2*2}=\frac{-81-3\sqrt{889}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+3\sqrt{889}}{2*2}=\frac{-81+3\sqrt{889}}{4}
$