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

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

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

We move all terms to the left:

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

We multiply parentheses

x^2+80x+(x-20)-180=0

We get rid of parentheses

x^2+80x+x-20-180=0

We add all the numbers together, and all the variables

x^2+81x-200=0

a = 1; b = 81; c = -200;
Δ = b2-4ac
Δ = 812-4·1·(-200)
Δ = 7361
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{-(81)-\sqrt{7361}}{2*1}=\frac{-81-\sqrt{7361}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+\sqrt{7361}}{2*1}=\frac{-81+\sqrt{7361}}{2}
$