b-11/3b=6

Solution for b-11/3b=6 equation:

b-11/3b=6

We move all terms to the left:

b-11/3b-(6)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We multiply all the terms by the denominator


b*3b-6*3b-11=0

Wy multiply elements

3b^2-18b-11=0

a = 3; b = -18; c = -11;
Δ = b2-4ac
Δ = -182-4·3·(-11)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{114}}{2*3}=\frac{18-2\sqrt{114}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{114}}{2*3}=\frac{18+2\sqrt{114}}{6}
$