(x^2)+12x+13=5+1

Solution for (x^2)+12x+13=5+1 equation:

(x^2)+12x+13=5+1

We move all terms to the left:

(x^2)+12x+13-(5+1)=0

We add all the numbers together, and all the variables

x^2+12x+13-6=0

We add all the numbers together, and all the variables

x^2+12x+7=0

a = 1; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·1·7
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{29}}{2*1}=\frac{-12-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{29}}{2*1}=\frac{-12+2\sqrt{29}}{2}
$