1.3x=54/x

Solution for 1.3x=54/x equation:

1.3x=54/x

We move all terms to the left:

1.3x-(54/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1.3x-(+54/x)=0

We get rid of parentheses

1.3x-54/x=0

We multiply all the terms by the denominator


(1.3x)*x-54=0

We add all the numbers together, and all the variables

(+1.3x)*x-54=0

We multiply parentheses

x^2-54=0

a = 1; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·1·(-54)
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*1}=\frac{0-6\sqrt{6}}{2}
=-\frac{6\sqrt{6}}{2}
=-3\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*1}=\frac{0+6\sqrt{6}}{2}
=\frac{6\sqrt{6}}{2}
=3\sqrt{6}
$