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

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

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

We move all terms to the left:

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


Domain of the equation: 7b!=0

b!=0/7

b!=0

b∈R



Domain of the equation: b-5)!=0

b∈R


We get rid of parentheses

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

We calculate fractions


7b/7b^2+(-14b)/7b^2+5+5=0

We add all the numbers together, and all the variables

7b/7b^2+(-14b)/7b^2+10=0

We multiply all the terms by the denominator


7b+(-14b)+10*7b^2=0

Wy multiply elements

70b^2+7b+(-14b)=0

We get rid of parentheses

70b^2+7b-14b=0

We add all the numbers together, and all the variables

70b^2-7b=0

a = 70; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·70·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*70}=\frac{0}{140}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*70}=\frac{14}{140}
=1/10
$