6b^2-8b=23

Solution for 6b^2-8b=23 equation:

6b^2-8b=23

We move all terms to the left:

6b^2-8b-(23)=0

a = 6; b = -8; c = -23;
Δ = b2-4ac
Δ = -82-4·6·(-23)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{154}}{2*6}=\frac{8-2\sqrt{154}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{154}}{2*6}=\frac{8+2\sqrt{154}}{12}
$