50(x+10)(x+20)=180

Solution for 50(x+10)(x+20)=180 equation:

50(x+10)(x+20)=180

We move all terms to the left:

50(x+10)(x+20)-(180)=0

We multiply parentheses ..

50(+x^2+20x+10x+200)-180=0

We multiply parentheses

50x^2+1000x+500x+10000-180=0

We add all the numbers together, and all the variables

50x^2+1500x+9820=0

a = 50; b = 1500; c = +9820;
Δ = b2-4ac
Δ = 15002-4·50·9820
Δ = 286000
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:

$\sqrt{\Delta}=\sqrt{286000}=\sqrt{400*715}=\sqrt{400}*\sqrt{715}=20\sqrt{715}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1500)-20\sqrt{715}}{2*50}=\frac{-1500-20\sqrt{715}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1500)+20\sqrt{715}}{2*50}=\frac{-1500+20\sqrt{715}}{100}
$