n^2-16n-32=-7

Solution for n^2-16n-32=-7 equation:

n^2-16n-32=-7

We move all terms to the left:

n^2-16n-32-(-7)=0

We add all the numbers together, and all the variables

n^2-16n-25=0

a = 1; b = -16; c = -25;
Δ = b2-4ac
Δ = -162-4·1·(-25)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{89}}{2*1}=\frac{16-2\sqrt{89}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{89}}{2*1}=\frac{16+2\sqrt{89}}{2}
$