X+1/9=2x/3x+6

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Solution for X+1/9=2x/3x+6 equation:



X+1/9=2X/3X+6
We move all terms to the left:
X+1/9-(2X/3X+6)=0
Domain of the equation: 3X+6)!=0
X∈R
We get rid of parentheses
X-2X/3X-6+1/9=0
We calculate fractions
X+(-18X)/27X+3X/27X-6=0
We multiply all the terms by the denominator
X*27X+(-18X)+3X-6*27X=0
We add all the numbers together, and all the variables
3X+X*27X+(-18X)-6*27X=0
Wy multiply elements
27X^2+3X+(-18X)-162X=0
We get rid of parentheses
27X^2+3X-18X-162X=0
We add all the numbers together, and all the variables
27X^2-177X=0
a = 27; b = -177; c = 0;
Δ = b2-4ac
Δ = -1772-4·27·0
Δ = 31329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{31329}=177$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-177)-177}{2*27}=\frac{0}{54} =0 $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-177)+177}{2*27}=\frac{354}{54} =6+5/9 $

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