(x+85)(x+20)=180

Solution for (x+85)(x+20)=180 equation:

(x+85)(x+20)=180

We move all terms to the left:

(x+85)(x+20)-(180)=0

We multiply parentheses ..

(+x^2+20x+85x+1700)-180=0

We get rid of parentheses

x^2+20x+85x+1700-180=0

We add all the numbers together, and all the variables

x^2+105x+1520=0

a = 1; b = 105; c = +1520;
Δ = b2-4ac
Δ = 1052-4·1·1520
Δ = 4945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-\sqrt{4945}}{2*1}=\frac{-105-\sqrt{4945}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{4945}}{2*1}=\frac{-105+\sqrt{4945}}{2}
$