6b^2=12b+39=0

Solution for 6b^2=12b+39=0 equation:

6b^2=12b+39=0

We move all terms to the left:

6b^2-(12b+39)=0

We get rid of parentheses

6b^2-12b-39=0

a = 6; b = -12; c = -39;
Δ = b2-4ac
Δ = -122-4·6·(-39)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{30}}{2*6}=\frac{12-6\sqrt{30}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{30}}{2*6}=\frac{12+6\sqrt{30}}{12}
$