3b+6=1/2b

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

3b+6=1/2b

We move all terms to the left:

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


Domain of the equation: 2b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3b-1/2b+6=0

We multiply all the terms by the denominator


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

Wy multiply elements

6b^2+12b-1=0

a = 6; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·6·(-1)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*6}=\frac{-12-2\sqrt{42}}{12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*6}=\frac{-12+2\sqrt{42}}{12}
$