10/3x-2=2x

Solution for 10/3x-2=2x equation:

10/3x-2=2x

We move all terms to the left:

10/3x-2-(2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+10/3x-2=0

We multiply all the terms by the denominator


-2x*3x-2*3x+10=0

Wy multiply elements

-6x^2-6x+10=0

a = -6; b = -6; c = +10;
Δ = b2-4ac
Δ = -62-4·(-6)·10
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{69}}{2*-6}=\frac{6-2\sqrt{69}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{69}}{2*-6}=\frac{6+2\sqrt{69}}{-12}
$