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

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

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

We move all terms to the left:

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


Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R



Domain of the equation: b-7)!=0

b∈R


We get rid of parentheses

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

We calculate fractions


6b/6b^2+(-12b)/6b^2+7+7=0

We add all the numbers together, and all the variables

6b/6b^2+(-12b)/6b^2+14=0

We multiply all the terms by the denominator


6b+(-12b)+14*6b^2=0

Wy multiply elements

84b^2+6b+(-12b)=0

We get rid of parentheses

84b^2+6b-12b=0

We add all the numbers together, and all the variables

84b^2-6b=0

a = 84; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·84·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*84}=\frac{0}{168}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*84}=\frac{12}{168}
=1/14
$