4b+1/3b-1=2

Solution for 4b+1/3b-1=2 equation:

4b+1/3b-1=2

We move all terms to the left:

4b+1/3b-1-(2)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

4b+1/3b-3=0

We multiply all the terms by the denominator


4b*3b-3*3b+1=0

Wy multiply elements

12b^2-9b+1=0

a = 12; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·12·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{33}}{2*12}=\frac{9-\sqrt{33}}{24}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*12}=\frac{9+\sqrt{33}}{24}
$