3/1-2x=-5/3x-2

Solution for 3/1-2x=-5/3x-2 equation:

3/1-2x=-5/3x-2

We move all terms to the left:

3/1-2x-(-5/3x-2)=0


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+6x+5=0

a = -6; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-6)·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*-6}=\frac{-6-2\sqrt{39}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*-6}=\frac{-6+2\sqrt{39}}{-12}
$