(2x+30)(x+80)=180

Solution for (2x+30)(x+80)=180 equation:

(2x+30)(x+80)=180

We move all terms to the left:

(2x+30)(x+80)-(180)=0

We multiply parentheses ..

(+2x^2+160x+30x+2400)-180=0

We get rid of parentheses

2x^2+160x+30x+2400-180=0

We add all the numbers together, and all the variables

2x^2+190x+2220=0

a = 2; b = 190; c = +2220;
Δ = b2-4ac
Δ = 1902-4·2·2220
Δ = 18340
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:

$\sqrt{\Delta}=\sqrt{18340}=\sqrt{4*4585}=\sqrt{4}*\sqrt{4585}=2\sqrt{4585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-2\sqrt{4585}}{2*2}=\frac{-190-2\sqrt{4585}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+2\sqrt{4585}}{2*2}=\frac{-190+2\sqrt{4585}}{4}
$