3*3x-5=1/9*x

Solution for 3*3x-5=1/9*x equation:

3*3x-5=1/9x

We move all terms to the left:

3*3x-5-(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

3*3x-(+1/9x)-5=0

Wy multiply elements

9x-(+1/9x)-5=0

We get rid of parentheses

9x-1/9x-5=0

We multiply all the terms by the denominator


9x*9x-5*9x-1=0

Wy multiply elements

81x^2-45x-1=0

a = 81; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·81·(-1)
Δ = 2349
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:

$\sqrt{\Delta}=\sqrt{2349}=\sqrt{81*29}=\sqrt{81}*\sqrt{29}=9\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-9\sqrt{29}}{2*81}=\frac{45-9\sqrt{29}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+9\sqrt{29}}{2*81}=\frac{45+9\sqrt{29}}{162}
$