2x(x+10)+80=180

Solution for 2x(x+10)+80=180 equation:

2x(x+10)+80=180

We move all terms to the left:

2x(x+10)+80-(180)=0

We add all the numbers together, and all the variables

2x(x+10)-100=0

We multiply parentheses

2x^2+20x-100=0

a = 2; b = 20; c = -100;
Δ = b2-4ac
Δ = 202-4·2·(-100)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{3}}{2*2}=\frac{-20-20\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{3}}{2*2}=\frac{-20+20\sqrt{3}}{4}
$