4x+20+x^2-12=180

Solution for 4x+20+x^2-12=180 equation:

4x+20+x^2-12=180

We move all terms to the left:

4x+20+x^2-12-(180)=0

We add all the numbers together, and all the variables

x^2+4x-172=0

a = 1; b = 4; c = -172;
Δ = b2-4ac
Δ = 42-4·1·(-172)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{11}}{2*1}=\frac{-4-8\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{11}}{2*1}=\frac{-4+8\sqrt{11}}{2}
$