1/b-1=b1+2

Solution for 1/b-1=b1+2 equation:

1/b-1=b1+2

We move all terms to the left:

1/b-1-(b1+2)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

1/b-(b+2)-1=0

We get rid of parentheses

1/b-b-2-1=0

We multiply all the terms by the denominator


-b*b-2*b-1*b+1=0

We add all the numbers together, and all the variables

-3b-b*b+1=0

Wy multiply elements

-1b^2-3b+1=0

a = -1; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-1)·1
Δ = 13
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{-(-3)-\sqrt{13}}{2*-1}=\frac{3-\sqrt{13}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{13}}{2*-1}=\frac{3+\sqrt{13}}{-2}
$