80(x+20)x=180

Solution for 80(x+20)x=180 equation:

80(x+20)x=180

We move all terms to the left:

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

We multiply parentheses

80x^2+1600x-180=0

a = 80; b = 1600; c = -180;
Δ = b2-4ac
Δ = 16002-4·80·(-180)
Δ = 2617600
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:

$\sqrt{\Delta}=\sqrt{2617600}=\sqrt{6400*409}=\sqrt{6400}*\sqrt{409}=80\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1600)-80\sqrt{409}}{2*80}=\frac{-1600-80\sqrt{409}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1600)+80\sqrt{409}}{2*80}=\frac{-1600+80\sqrt{409}}{160}
$