96/b=22-b

Solution for 96/b=22-b equation:

96/b=22-b

We move all terms to the left:

96/b-(22-b)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

96/b-(-1b+22)=0

We get rid of parentheses

96/b+1b-22=0

We multiply all the terms by the denominator


1b*b-22*b+96=0

We add all the numbers together, and all the variables

-22b+1b*b+96=0

Wy multiply elements

b^2-22b+96=0

a = 1; b = -22; c = +96;
Δ = b2-4ac
Δ = -222-4·1·96
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-10}{2*1}=\frac{12}{2}
=6
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10}{2*1}=\frac{32}{2}
=16
$