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

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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} $

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