x+x(x+30)=180

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

x+x(x+30)=180

We move all terms to the left:

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

We multiply parentheses

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

We add all the numbers together, and all the variables

x^2+31x-180=0

a = 1; b = 31; c = -180;
Δ = b2-4ac
Δ = 312-4·1·(-180)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-41}{2*1}=\frac{-72}{2}
=-36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+41}{2*1}=\frac{10}{2}
=5
$