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

Solution for b/2b-(6+6b)=2/7 equation:

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

We move all terms to the left:

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


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

b/2b-6b-6-2/7=0

We calculate fractions


-6b+7b/14b+(-4b)/14b-6=0

We multiply all the terms by the denominator


-6b*14b+7b+(-4b)-6*14b=0

We add all the numbers together, and all the variables

7b-6b*14b+(-4b)-6*14b=0

Wy multiply elements

-84b^2+7b+(-4b)-84b=0

We get rid of parentheses

-84b^2+7b-4b-84b=0

We add all the numbers together, and all the variables

-84b^2-81b=0

a = -84; b = -81; c = 0;
Δ = b2-4ac
Δ = -812-4·(-84)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-81}{2*-84}=\frac{0}{-168}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+81}{2*-84}=\frac{162}{-168}
=-27/28
$