4/b-2=3-b

Solution for 4/b-2=3-b equation:

4/b-2=3-b

We move all terms to the left:

4/b-2-(3-b)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

4/b-(-1b+3)-2=0

We get rid of parentheses

4/b+1b-3-2=0

We multiply all the terms by the denominator


1b*b-3*b-2*b+4=0

We add all the numbers together, and all the variables

-5b+1b*b+4=0

Wy multiply elements

b^2-5b+4=0

a = 1; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·1·4
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{-(-5)-3}{2*1}=\frac{2}{2}
=1
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*1}=\frac{8}{2}
=4
$