x=180-x^2-12

Solution for x=180-x^2-12 equation:

x=180-x^2-12

We move all terms to the left:

x-(180-x^2-12)=0

We get rid of parentheses

x^2+x-180+12=0

We add all the numbers together, and all the variables

x^2+x-168=0

a = 1; b = 1; c = -168;
Δ = b2-4ac
Δ = 12-4·1·(-168)
Δ = 673
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{-(1)-\sqrt{673}}{2*1}=\frac{-1-\sqrt{673}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{673}}{2*1}=\frac{-1+\sqrt{673}}{2}
$