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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x+x(x+30)-180=0

We multiply parentheses

x^2+3x+30x-180=0

We add all the numbers together, and all the variables

x^2+33x-180=0

a = 1; b = 33; c = -180;
Δ = b2-4ac
Δ = 332-4·1·(-180)
Δ = 1809
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:

$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{201}}{2*1}=\frac{-33-3\sqrt{201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{201}}{2*1}=\frac{-33+3\sqrt{201}}{2}
$