3x+2/3x+2=5x-10/3x-2

Solution for 3x+2/3x+2=5x-10/3x-2 equation:

3x+2/3x+2=5x-10/3x-2

We move all terms to the left:

3x+2/3x+2-(5x-10/3x-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

3x+2/3x-5x+10/3x+2+2=0

We multiply all the terms by the denominator


3x*3x-5x*3x+2*3x+2*3x+2+10=0

We add all the numbers together, and all the variables

3x*3x-5x*3x+2*3x+2*3x+12=0

Wy multiply elements

9x^2-15x^2+6x+6x+12=0

We add all the numbers together, and all the variables

-6x^2+12x+12=0

a = -6; b = 12; c = +12;
Δ = b2-4ac
Δ = 122-4·(-6)·12
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{3}}{2*-6}=\frac{-12-12\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{3}}{2*-6}=\frac{-12+12\sqrt{3}}{-12}
$