6b^2-6b-5=0

Solution for 6b^2-6b-5=0 equation:

6b^2-6b-5=0

a = 6; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·6·(-5)
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*6}=\frac{6-2\sqrt{39}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*6}=\frac{6+2\sqrt{39}}{12}
$