4/3x-9=8-3/6x

Solution for 4/3x-9=8-3/6x equation:

4/3x-9=8-3/6x

We move all terms to the left:

4/3x-9-(8-3/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-3/6x+8)-9=0

We get rid of parentheses

4/3x+3/6x-8-9=0

We calculate fractions


24x/18x^2+9x/18x^2-8-9=0

We add all the numbers together, and all the variables

24x/18x^2+9x/18x^2-17=0

We multiply all the terms by the denominator


24x+9x-17*18x^2=0

We add all the numbers together, and all the variables

33x-17*18x^2=0

Wy multiply elements

-306x^2+33x=0

a = -306; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-306)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-306}=\frac{-66}{-612}
=11/102
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-306}=\frac{0}{-612}
=0
$