6b=7+2/3b

Solution for 6b=7+2/3b equation:

6b=7+2/3b

We move all terms to the left:

6b-(7+2/3b)=0


Domain of the equation: 3b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

6b-(2/3b+7)=0

We get rid of parentheses

6b-2/3b-7=0

We multiply all the terms by the denominator


6b*3b-7*3b-2=0

Wy multiply elements

18b^2-21b-2=0

a = 18; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·18·(-2)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{65}}{2*18}=\frac{21-3\sqrt{65}}{36}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{65}}{2*18}=\frac{21+3\sqrt{65}}{36}
$