(x-30)(x+50)=180

Solution for (x-30)(x+50)=180 equation:

(x-30)(x+50)=180

We move all terms to the left:

(x-30)(x+50)-(180)=0

We multiply parentheses ..

(+x^2+50x-30x-1500)-180=0

We get rid of parentheses

x^2+50x-30x-1500-180=0

We add all the numbers together, and all the variables

x^2+20x-1680=0

a = 1; b = 20; c = -1680;
Δ = b2-4ac
Δ = 202-4·1·(-1680)
Δ = 7120
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:

$\sqrt{\Delta}=\sqrt{7120}=\sqrt{16*445}=\sqrt{16}*\sqrt{445}=4\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{445}}{2*1}=\frac{-20-4\sqrt{445}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{445}}{2*1}=\frac{-20+4\sqrt{445}}{2}
$