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

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

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

We move all terms to the left:

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


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

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

b!=-7

b∈R



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

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

10b^2+7b+(-2b-14)+70b=0

We get rid of parentheses

10b^2+7b-2b+70b-14=0

We add all the numbers together, and all the variables

10b^2+75b-14=0

a = 10; b = 75; c = -14;
Δ = b2-4ac
Δ = 752-4·10·(-14)
Δ = 6185
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{-(75)-\sqrt{6185}}{2*10}=\frac{-75-\sqrt{6185}}{20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{6185}}{2*10}=\frac{-75+\sqrt{6185}}{20}
$