2s^2+26s-1=0

Solution for 2s^2+26s-1=0 equation:

2s^2+26s-1=0

a = 2; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·2·(-1)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6\sqrt{19}}{2*2}=\frac{-26-6\sqrt{19}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6\sqrt{19}}{2*2}=\frac{-26+6\sqrt{19}}{4}
$