72/b=4;b=1,3,4,9

Solution for 72/b=4;b=1,3,4,9 equation:

72/b=4b=1.3.4.9

We move all terms to the left:

72/b-(4b)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

-4b+72/b=0

We multiply all the terms by the denominator


-4b*b+72=0

Wy multiply elements

-4b^2+72=0

a = -4; b = 0; c = +72;
Δ = b2-4ac
Δ = 02-4·(-4)·72
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-4}=\frac{0-24\sqrt{2}}{-8}
=-\frac{24\sqrt{2}}{-8}
=-\frac{3\sqrt{2}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-4}=\frac{0+24\sqrt{2}}{-8}
=\frac{24\sqrt{2}}{-8}
=\frac{3\sqrt{2}}{-1}
$