5/3x=2x-2/3x+2

Solution for 5/3x=2x-2/3x+2 equation:

5/3x=2x-2/3x+2

We move all terms to the left:

5/3x-(2x-2/3x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

5/3x-2x+2/3x-2=0

We multiply all the terms by the denominator


-2x*3x-2*3x+5+2=0

We add all the numbers together, and all the variables

-2x*3x-2*3x+7=0

Wy multiply elements

-6x^2-6x+7=0

a = -6; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-6)·7
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{51}}{2*-6}=\frac{6-2\sqrt{51}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{51}}{2*-6}=\frac{6+2\sqrt{51}}{-12}
$