4/9x-8-1/3x=3

Solution for 4/9x-8-1/3x=3 equation:

4/9x-8-1/3x=3

We move all terms to the left:

4/9x-8-1/3x-(3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/9x-1/3x-11=0

We calculate fractions


12x/27x^2+(-9x)/27x^2-11=0

We multiply all the terms by the denominator


12x+(-9x)-11*27x^2=0

Wy multiply elements

-297x^2+12x+(-9x)=0

We get rid of parentheses

-297x^2+12x-9x=0

We add all the numbers together, and all the variables

-297x^2+3x=0

a = -297; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-297)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-297}=\frac{-6}{-594}
=1/99
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-297}=\frac{0}{-594}
=0
$