54=18/b^2(b^3)

Solution for 54=18/b^2(b^3) equation:

54=18/b^2(b^3)

We move all terms to the left:

54-(18/b^2(b^3))=0


Domain of the equation: b^2b^3)!=0

b!=0/1

b!=0

b∈R


We get rid of parentheses

-18/b^2b^3+54=0

We multiply all the terms by the denominator


54*b^2b^3-18=0

Wy multiply elements

54b^2-18=0

a = 54; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·54·(-18)
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{3}}{2*54}=\frac{0-36\sqrt{3}}{108}
=-\frac{36\sqrt{3}}{108}
=-\frac{\sqrt{3}}{3}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{3}}{2*54}=\frac{0+36\sqrt{3}}{108}
=\frac{36\sqrt{3}}{108}
=\frac{\sqrt{3}}{3}
$