(3x)(x+20)+100=180

Solution for (3x)(x+20)+100=180 equation:

(3x)(x+20)+100=180

We move all terms to the left:

(3x)(x+20)+100-(180)=0

We add all the numbers together, and all the variables

3x(x+20)-80=0

We multiply parentheses

3x^2+60x-80=0

a = 3; b = 60; c = -80;
Δ = b2-4ac
Δ = 602-4·3·(-80)
Δ = 4560
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:

$\sqrt{\Delta}=\sqrt{4560}=\sqrt{16*285}=\sqrt{16}*\sqrt{285}=4\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{285}}{2*3}=\frac{-60-4\sqrt{285}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{285}}{2*3}=\frac{-60+4\sqrt{285}}{6}
$