6x-1=1/9x

Solution for 6x-1=1/9x equation:

6x-1=1/9x

We move all terms to the left:

6x-1-(1/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+1/9x)-1=0

We get rid of parentheses

6x-1/9x-1=0

We multiply all the terms by the denominator


6x*9x-1*9x-1=0

Wy multiply elements

54x^2-9x-1=0

a = 54; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·54·(-1)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{33}}{2*54}=\frac{9-3\sqrt{33}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{33}}{2*54}=\frac{9+3\sqrt{33}}{108}
$