x^2+10x+26=8

Solution for x^2+10x+26=8 equation:

x^2+10x+26=8

We move all terms to the left:

x^2+10x+26-(8)=0

We add all the numbers together, and all the variables

x^2+10x+18=0

a = 1; b = 10; c = +18;
Δ = b2-4ac
Δ = 102-4·1·18
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*1}=\frac{-10-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*1}=\frac{-10+2\sqrt{7}}{2}
$