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

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
$