p2-12p=-13

Solution for p2-12p=-13 equation:

p2-12p=-13

We move all terms to the left:

p2-12p-(-13)=0

We add all the numbers together, and all the variables

p^2-12p+13=0

a = 1; b = -12; c = +13;
Δ = b2-4ac
Δ = -122-4·1·13
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{23}}{2*1}=\frac{12-2\sqrt{23}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{23}}{2*1}=\frac{12+2\sqrt{23}}{2}
$