(x+4)+x(x+32)=180

Solution for (x+4)+x(x+32)=180 equation:

(x+4)+x(x+32)=180

We move all terms to the left:

(x+4)+x(x+32)-(180)=0

We multiply parentheses

x^2+(x+4)+32x-180=0

We get rid of parentheses

x^2+x+32x+4-180=0

We add all the numbers together, and all the variables

x^2+33x-176=0

a = 1; b = 33; c = -176;
Δ = b2-4ac
Δ = 332-4·1·(-176)
Δ = 1793
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1793}}{2*1}=\frac{-33-\sqrt{1793}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1793}}{2*1}=\frac{-33+\sqrt{1793}}{2}
$