5s^2-14s-5=0

Solution for 5s^2-14s-5=0 equation:

5s^2-14s-5=0

a = 5; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·5·(-5)
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{74}}{2*5}=\frac{14-2\sqrt{74}}{10}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{74}}{2*5}=\frac{14+2\sqrt{74}}{10}
$