6s^2-6s-3=0

Solution for 6s^2-6s-3=0 equation:

6s^2-6s-3=0

a = 6; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·6·(-3)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*6}=\frac{6-6\sqrt{3}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*6}=\frac{6+6\sqrt{3}}{12}
$