2/3x-4/9x+6=11

Solution for 2/3x-4/9x+6=11 equation:

2/3x-4/9x+6=11

We move all terms to the left:

2/3x-4/9x+6-(11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-4/9x-5=0

We calculate fractions


18x/27x^2+(-12x)/27x^2-5=0

We multiply all the terms by the denominator


18x+(-12x)-5*27x^2=0

Wy multiply elements

-135x^2+18x+(-12x)=0

We get rid of parentheses

-135x^2+18x-12x=0

We add all the numbers together, and all the variables

-135x^2+6x=0

a = -135; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-135)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-135}=\frac{-12}{-270}
=2/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-135}=\frac{0}{-270}
=0
$