n^2+8n-11=-5

Solution for n^2+8n-11=-5 equation:

n^2+8n-11=-5

We move all terms to the left:

n^2+8n-11-(-5)=0

We add all the numbers together, and all the variables

n^2+8n-6=0

a = 1; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·1·(-6)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*1}=\frac{-8-2\sqrt{22}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*1}=\frac{-8+2\sqrt{22}}{2}
$