7s^2-2s-1=0

Solution for 7s^2-2s-1=0 equation:

7s^2-2s-1=0

a = 7; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·7·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{2}}{2*7}=\frac{2-4\sqrt{2}}{14}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{2}}{2*7}=\frac{2+4\sqrt{2}}{14}
$