n2+8n-26=0

Solution for n2+8n-26=0 equation:

n2+8n-26=0

We add all the numbers together, and all the variables

n^2+8n-26=0

a = 1; b = 8; c = -26;
Δ = b2-4ac
Δ = 82-4·1·(-26)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{42}}{2*1}=\frac{-8-2\sqrt{42}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{42}}{2*1}=\frac{-8+2\sqrt{42}}{2}
$