n2+6n-94=-8

Solution for n2+6n-94=-8 equation:

n2+6n-94=-8

We move all terms to the left:

n2+6n-94-(-8)=0

We add all the numbers together, and all the variables

n^2+6n-86=0

a = 1; b = 6; c = -86;
Δ = b2-4ac
Δ = 62-4·1·(-86)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{95}}{2*1}=\frac{-6-2\sqrt{95}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{95}}{2*1}=\frac{-6+2\sqrt{95}}{2}
$