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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-18x)/27x^2+(-12x)/27x^2+3+9=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

324x^2+(-18x)+(-12x)=0

We get rid of parentheses

324x^2-18x-12x=0

We add all the numbers together, and all the variables

324x^2-30x=0

a = 324; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·324·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*324}=\frac{60}{648}
=5/54
$