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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2/3x-6x+2+9=0

We multiply all the terms by the denominator


-6x*3x+2*3x+9*3x-2=0

Wy multiply elements

-18x^2+6x+27x-2=0

We add all the numbers together, and all the variables

-18x^2+33x-2=0

a = -18; b = 33; c = -2;
Δ = b2-4ac
Δ = 332-4·(-18)·(-2)
Δ = 945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{105}}{2*-18}=\frac{-33-3\sqrt{105}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{105}}{2*-18}=\frac{-33+3\sqrt{105}}{-36}
$