40+4x(x+20)=180

Solution for 40+4x(x+20)=180 equation:

40+4x(x+20)=180

We move all terms to the left:

40+4x(x+20)-(180)=0

We add all the numbers together, and all the variables

4x(x+20)-140=0

We multiply parentheses

4x^2+80x-140=0

a = 4; b = 80; c = -140;
Δ = b2-4ac
Δ = 802-4·4·(-140)
Δ = 8640
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:

$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-24\sqrt{15}}{2*4}=\frac{-80-24\sqrt{15}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+24\sqrt{15}}{2*4}=\frac{-80+24\sqrt{15}}{8}
$