1/2b-2/3=5/6b

Solution for 1/2b-2/3=5/6b equation:

1/2b-2/3=5/6b

We move all terms to the left:

1/2b-2/3-(5/6b)=0


Domain of the equation: 2b!=0

b!=0/2

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

1/2b-(+5/6b)-2/3=0

We get rid of parentheses

1/2b-5/6b-2/3=0

We calculate fractions


(-144b^2)/108b^2+54b/108b^2+(-90b)/108b^2=0

We multiply all the terms by the denominator


(-144b^2)+54b+(-90b)=0

We get rid of parentheses

-144b^2+54b-90b=0

We add all the numbers together, and all the variables

-144b^2-36b=0

a = -144; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-144)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-144}=\frac{0}{-288}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-144}=\frac{72}{-288}
=-1/4
$