2/3b=6-5/6b

Solution for 2/3b=6-5/6b equation:

2/3b=6-5/6b

We move all terms to the left:

2/3b-(6-5/6b)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 6b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

2/3b-(-5/6b+6)=0

We get rid of parentheses

2/3b+5/6b-6=0

We calculate fractions


12b/18b^2+15b/18b^2-6=0

We multiply all the terms by the denominator


12b+15b-6*18b^2=0

We add all the numbers together, and all the variables

27b-6*18b^2=0

Wy multiply elements

-108b^2+27b=0

a = -108; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-108)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-108}=\frac{-54}{-216}
=1/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-108}=\frac{0}{-216}
=0
$