7/5b+9=2/7b

Solution for 7/5b+9=2/7b equation:

7/5b+9=2/7b

We move all terms to the left:

7/5b+9-(2/7b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 7b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

7/5b-(+2/7b)+9=0

We get rid of parentheses

7/5b-2/7b+9=0

We calculate fractions


49b/35b^2+(-10b)/35b^2+9=0

We multiply all the terms by the denominator


49b+(-10b)+9*35b^2=0

Wy multiply elements

315b^2+49b+(-10b)=0

We get rid of parentheses

315b^2+49b-10b=0

We add all the numbers together, and all the variables

315b^2+39b=0

a = 315; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·315·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*315}=\frac{-78}{630}
=-13/105
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*315}=\frac{0}{630}
=0
$