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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-6x)/27x^2+(-36x)/27x^2+3+9=0

We add all the numbers together, and all the variables

(-6x)/27x^2+(-36x)/27x^2+12=0

We multiply all the terms by the denominator


(-6x)+(-36x)+12*27x^2=0

Wy multiply elements

324x^2+(-6x)+(-36x)=0

We get rid of parentheses

324x^2-6x-36x=0

We add all the numbers together, and all the variables

324x^2-42x=0

a = 324; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·324·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*324}=\frac{84}{648}
=7/54
$