1/2b+3=5/7b+-1

Solution for 1/2b+3=5/7b+-1 equation:

1/2b+3=5/7b+-1

We move all terms to the left:

1/2b+3-(5/7b+-1)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 7b+-1)!=0

b∈R


We add all the numbers together, and all the variables

1/2b-(5/7b-1)+3=0

We get rid of parentheses

1/2b-5/7b+1+3=0

We calculate fractions


7b/14b^2+(-10b)/14b^2+1+3=0

We add all the numbers together, and all the variables

7b/14b^2+(-10b)/14b^2+4=0

We multiply all the terms by the denominator


7b+(-10b)+4*14b^2=0

Wy multiply elements

56b^2+7b+(-10b)=0

We get rid of parentheses

56b^2+7b-10b=0

We add all the numbers together, and all the variables

56b^2-3b=0

a = 56; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·56·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*56}=\frac{0}{112}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*56}=\frac{6}{112}
=3/56
$