5x=18/x

Solution for 5x=18/x equation:

5x=18/x

We move all terms to the left:

5x-(18/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

5x-(+18/x)=0

We get rid of parentheses

5x-18/x=0

We multiply all the terms by the denominator


5x*x-18=0

Wy multiply elements

5x^2-18=0

a = 5; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·5·(-18)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*5}=\frac{0-6\sqrt{10}}{10}
=-\frac{6\sqrt{10}}{10}
=-\frac{3\sqrt{10}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*5}=\frac{0+6\sqrt{10}}{10}
=\frac{6\sqrt{10}}{10}
=\frac{3\sqrt{10}}{5}
$