(x+20)(6x-180)=30000

Solution for (x+20)(6x-180)=30000 equation:

(x+20)(6x-180)=30000

We move all terms to the left:

(x+20)(6x-180)-(30000)=0

We multiply parentheses ..

(+6x^2-180x+120x-3600)-30000=0

We get rid of parentheses

6x^2-180x+120x-3600-30000=0

We add all the numbers together, and all the variables

6x^2-60x-33600=0

a = 6; b = -60; c = -33600;
Δ = b2-4ac
Δ = -602-4·6·(-33600)
Δ = 810000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{810000}=900$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-900}{2*6}=\frac{-840}{12}
=-70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+900}{2*6}=\frac{960}{12}
=80
$