9s^2-2s-5=0

Solution for 9s^2-2s-5=0 equation:

9s^2-2s-5=0

a = 9; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·9·(-5)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{46}}{2*9}=\frac{2-2\sqrt{46}}{18}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{46}}{2*9}=\frac{2+2\sqrt{46}}{18}
$