6b-1=2/3b+11

Solution for 6b-1=2/3b+11 equation:

6b-1=2/3b+11

We move all terms to the left:

6b-1-(2/3b+11)=0


Domain of the equation: 3b+11)!=0

b∈R


We get rid of parentheses

6b-2/3b-11-1=0

We multiply all the terms by the denominator


6b*3b-11*3b-1*3b-2=0

Wy multiply elements

18b^2-33b-3b-2=0

We add all the numbers together, and all the variables

18b^2-36b-2=0

a = 18; b = -36; c = -2;
Δ = b2-4ac
Δ = -362-4·18·(-2)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{10}}{2*18}=\frac{36-12\sqrt{10}}{36}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{10}}{2*18}=\frac{36+12\sqrt{10}}{36}
$