15/7b+5=5/2b+1

Solution for 15/7b+5=5/2b+1 equation:

15/7b+5=5/2b+1

We move all terms to the left:

15/7b+5-(5/2b+1)=0


Domain of the equation: 7b!=0

b!=0/7

b!=0

b∈R



Domain of the equation: 2b+1)!=0

b∈R


We get rid of parentheses

15/7b-5/2b-1+5=0

We calculate fractions


30b/14b^2+(-35b)/14b^2-1+5=0

We add all the numbers together, and all the variables

30b/14b^2+(-35b)/14b^2+4=0

We multiply all the terms by the denominator


30b+(-35b)+4*14b^2=0

Wy multiply elements

56b^2+30b+(-35b)=0

We get rid of parentheses

56b^2+30b-35b=0

We add all the numbers together, and all the variables

56b^2-5b=0

a = 56; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·56·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*56}=\frac{0}{112}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*56}=\frac{10}{112}
=5/56
$