8/9x+5=4/3x-3

Solution for 8/9x+5=4/3x-3 equation:

8/9x+5=4/3x-3

We move all terms to the left:

8/9x+5-(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

8/9x-4/3x+3+5=0

We calculate fractions


24x/27x^2+(-36x)/27x^2+3+5=0

We add all the numbers together, and all the variables

24x/27x^2+(-36x)/27x^2+8=0

We multiply all the terms by the denominator


24x+(-36x)+8*27x^2=0

Wy multiply elements

216x^2+24x+(-36x)=0

We get rid of parentheses

216x^2+24x-36x=0

We add all the numbers together, and all the variables

216x^2-12x=0

a = 216; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·216·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*216}=\frac{0}{432}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*216}=\frac{24}{432}
=1/18
$