8+1/5b=31/0b

Solution for 8+1/5b=31/0b equation:

8+1/5b=31/0b

We move all terms to the left:

8+1/5b-(31/0b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 0b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

1/5b-(+31/0b)+8=0

We get rid of parentheses

1/5b-31/0b+8=0

We calculate fractions


b/b^2+(-155b)/b^2+8=0

We multiply all the terms by the denominator


b+(-155b)+8*b^2=0

We add all the numbers together, and all the variables

8b^2+b+(-155b)=0

We get rid of parentheses

8b^2+b-155b=0

We add all the numbers together, and all the variables

8b^2-154b=0

a = 8; b = -154; c = 0;
Δ = b2-4ac
Δ = -1542-4·8·0
Δ = 23716
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23716}=154$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-154}{2*8}=\frac{0}{16}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+154}{2*8}=\frac{308}{16}
=19+1/4
$