8/9x+4=2/3x-9

Solution for 8/9x+4=2/3x-9 equation:

8/9x+4=2/3x-9

We move all terms to the left:

8/9x+4-(2/3x-9)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



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

x∈R


We get rid of parentheses

8/9x-2/3x+9+4=0

We calculate fractions


24x/27x^2+(-18x)/27x^2+9+4=0

We add all the numbers together, and all the variables

24x/27x^2+(-18x)/27x^2+13=0

We multiply all the terms by the denominator


24x+(-18x)+13*27x^2=0

Wy multiply elements

351x^2+24x+(-18x)=0

We get rid of parentheses

351x^2+24x-18x=0

We add all the numbers together, and all the variables

351x^2+6x=0

a = 351; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·351·0
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*351}=\frac{-12}{702}
=-2/117
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*351}=\frac{0}{702}
=0
$