2s^2-8s=26

Solution for 2s^2-8s=26 equation:

2s^2-8s=26

We move all terms to the left:

2s^2-8s-(26)=0

a = 2; b = -8; c = -26;
Δ = b2-4ac
Δ = -82-4·2·(-26)
Δ = 272
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{17}}{2*2}=\frac{8-4\sqrt{17}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{17}}{2*2}=\frac{8+4\sqrt{17}}{4}
$