x2+2(K+-4)*x+K2+6K+3=0

Solution for x2+2(K+-4)*x+K2+6K+3=0 equation:

x2+2(+-4)*x+2+6+3=0

We add all the numbers together, and all the variables

x2+2(-4)*x+2+6+3=0

We add all the numbers together, and all the variables

x^2+2(-4)*x+11=0

We multiply parentheses

x^2-8x+11=0

a = 1; b = -8; c = +11;
Δ = b2-4ac
Δ = -82-4·1·11
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{5}}{2*1}=\frac{8-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{5}}{2*1}=\frac{8+2\sqrt{5}}{2}
$