n^2-12n-73=-11

Solution for n^2-12n-73=-11 equation:

n^2-12n-73=-11

We move all terms to the left:

n^2-12n-73-(-11)=0

We add all the numbers together, and all the variables

n^2-12n-62=0

a = 1; b = -12; c = -62;
Δ = b2-4ac
Δ = -122-4·1·(-62)
Δ = 392
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-14\sqrt{2}}{2*1}=\frac{12-14\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+14\sqrt{2}}{2*1}=\frac{12+14\sqrt{2}}{2}
$