40+2x(20+x)=180

Solution for 40+2x(20+x)=180 equation:

40+2x(20+x)=180

We move all terms to the left:

40+2x(20+x)-(180)=0

We add all the numbers together, and all the variables

2x(x+20)+40-180=0

We add all the numbers together, and all the variables

2x(x+20)-140=0

We multiply parentheses

2x^2+40x-140=0

a = 2; b = 40; c = -140;
Δ = b2-4ac
Δ = 402-4·2·(-140)
Δ = 2720
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:

$\sqrt{\Delta}=\sqrt{2720}=\sqrt{16*170}=\sqrt{16}*\sqrt{170}=4\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{170}}{2*2}=\frac{-40-4\sqrt{170}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{170}}{2*2}=\frac{-40+4\sqrt{170}}{4}
$