n^2-6n-89=-5

Solution for n^2-6n-89=-5 equation:

n^2-6n-89=-5

We move all terms to the left:

n^2-6n-89-(-5)=0

We add all the numbers together, and all the variables

n^2-6n-84=0

a = 1; b = -6; c = -84;
Δ = b2-4ac
Δ = -62-4·1·(-84)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{93}}{2*1}=\frac{6-2\sqrt{93}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{93}}{2*1}=\frac{6+2\sqrt{93}}{2}
$