6x=23/x=

Solution for 6x=23/x= equation:

6x=23/x=

We move all terms to the left:

6x-(23/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

6x-(+23/x)=0

We get rid of parentheses

6x-23/x=0

We multiply all the terms by the denominator


6x*x-23=0

Wy multiply elements

6x^2-23=0

a = 6; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·6·(-23)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{138}}{2*6}=\frac{0-2\sqrt{138}}{12}
=-\frac{2\sqrt{138}}{12}
=-\frac{\sqrt{138}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{138}}{2*6}=\frac{0+2\sqrt{138}}{12}
=\frac{2\sqrt{138}}{12}
=\frac{\sqrt{138}}{6}
$