6+1/2b=5/6b

Solution for 6+1/2b=5/6b equation:

6+1/2b=5/6b

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


6b/12b^2+(-10b)/12b^2+6=0

We multiply all the terms by the denominator


6b+(-10b)+6*12b^2=0

Wy multiply elements

72b^2+6b+(-10b)=0

We get rid of parentheses

72b^2+6b-10b=0

We add all the numbers together, and all the variables

72b^2-4b=0

a = 72; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·72·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*72}=\frac{0}{144}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*72}=\frac{8}{144}
=1/18
$