6/7b-10+3/7b=12+13/21b

Solution for 6/7b-10+3/7b=12+13/21b equation:

6/7b-10+3/7b=12+13/21b

We move all terms to the left:

6/7b-10+3/7b-(12+13/21b)=0


Domain of the equation: 7b!=0

b!=0/7

b!=0

b∈R



Domain of the equation: 21b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

6/7b+3/7b-(13/21b+12)-10=0

We get rid of parentheses

6/7b+3/7b-13/21b-12-10=0

We calculate fractions


(63b+6)/147b^2+(-91b)/147b^2-12-10=0

We add all the numbers together, and all the variables

(63b+6)/147b^2+(-91b)/147b^2-22=0

We multiply all the terms by the denominator


(63b+6)+(-91b)-22*147b^2=0

Wy multiply elements

-3234b^2+(63b+6)+(-91b)=0

We get rid of parentheses

-3234b^2+63b-91b+6=0

We add all the numbers together, and all the variables

-3234b^2-28b+6=0

a = -3234; b = -28; c = +6;
Δ = b2-4ac
Δ = -282-4·(-3234)·6
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-280}{2*-3234}=\frac{-252}{-6468}
=3/77
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+280}{2*-3234}=\frac{308}{-6468}
=-1/21
$