(x+23)(x+23)+36=180

Solution for (x+23)(x+23)+36=180 equation:

(x+23)(x+23)+36=180

We move all terms to the left:

(x+23)(x+23)+36-(180)=0

We add all the numbers together, and all the variables

(x+23)(x+23)-144=0

We multiply parentheses ..

(+x^2+23x+23x+529)-144=0

We get rid of parentheses

x^2+23x+23x+529-144=0

We add all the numbers together, and all the variables

x^2+46x+385=0

a = 1; b = 46; c = +385;
Δ = b2-4ac
Δ = 462-4·1·385
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-24}{2*1}=\frac{-70}{2}
=-35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+24}{2*1}=\frac{-22}{2}
=-11
$