x^2+20x+1=-3

Solution for x^2+20x+1=-3 equation:

x^2+20x+1=-3

We move all terms to the left:

x^2+20x+1-(-3)=0

We add all the numbers together, and all the variables

x^2+20x+4=0

a = 1; b = 20; c = +4;
Δ = b2-4ac
Δ = 202-4·1·4
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{6}}{2*1}=\frac{-20-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{6}}{2*1}=\frac{-20+8\sqrt{6}}{2}
$