48/b=14-b

Solution for 48/b=14-b equation:

48/b=14-b

We move all terms to the left:

48/b-(14-b)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

48/b-(-1b+14)=0

We get rid of parentheses

48/b+1b-14=0

We multiply all the terms by the denominator


1b*b-14*b+48=0

We add all the numbers together, and all the variables

-14b+1b*b+48=0

Wy multiply elements

b^2-14b+48=0

a = 1; b = -14; c = +48;
Δ = b2-4ac
Δ = -142-4·1·48
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2}{2*1}=\frac{12}{2}
=6
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*1}=\frac{16}{2}
=8
$