n^2-10n-86=-4

Solution for n^2-10n-86=-4 equation:

n^2-10n-86=-4

We move all terms to the left:

n^2-10n-86-(-4)=0

We add all the numbers together, and all the variables

n^2-10n-82=0

a = 1; b = -10; c = -82;
Δ = b2-4ac
Δ = -102-4·1·(-82)
Δ = 428
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:

$\sqrt{\Delta}=\sqrt{428}=\sqrt{4*107}=\sqrt{4}*\sqrt{107}=2\sqrt{107}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{107}}{2*1}=\frac{10-2\sqrt{107}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{107}}{2*1}=\frac{10+2\sqrt{107}}{2}
$