7/(7b+4)=2/b-4

Solution for 7/(7b+4)=2/b-4 equation:

7/(7b+4)=2/b-4

We move all terms to the left:

7/(7b+4)-(2/b-4)=0


Domain of the equation: (7b+4)!=0

We move all terms containing b to the left, all other terms to the right

7b!=-4

b!=-4/7

b!=-4/7

b∈R



Domain of the equation: b-4)!=0

b∈R


We get rid of parentheses

7/(7b+4)-2/b+4=0

We calculate fractions


7b/(7b^2+4b)+(-14b-8)/(7b^2+4b)+4=0

We multiply all the terms by the denominator


7b+(-14b-8)+4*(7b^2+4b)=0

We multiply parentheses

28b^2+7b+(-14b-8)+16b=0

We get rid of parentheses

28b^2+7b-14b+16b-8=0

We add all the numbers together, and all the variables

28b^2+9b-8=0

a = 28; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·28·(-8)
Δ = 977
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{977}}{2*28}=\frac{-9-\sqrt{977}}{56}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{977}}{2*28}=\frac{-9+\sqrt{977}}{56}
$