5/b-2=4/1+b

Solution for 5/b-2=4/1+b equation:

5/b-2=4/1+b

We move all terms to the left:

5/b-2-(4/1+b)=0


Domain of the equation: b!=0

b∈R



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

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

b)!=-1

b!=-1/1

b!=-1

b∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5/b-b-2=0

We multiply all the terms by the denominator


-b*b-2*b+5=0

We add all the numbers together, and all the variables

-2b-b*b+5=0

Wy multiply elements

-1b^2-2b+5=0

a = -1; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-1)·5
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*-1}=\frac{2-2\sqrt{6}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*-1}=\frac{2+2\sqrt{6}}{-2}
$