3x-2/2x+3=3x-12x+1

Solution for 3x-2/2x+3=3x-12x+1 equation:

3x-2/2x+3=3x-12x+1

We move all terms to the left:

3x-2/2x+3-(3x-12x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/2x-(-9x+1)+3=0

We get rid of parentheses

3x-2/2x+9x-1+3=0

We multiply all the terms by the denominator


3x*2x+9x*2x-1*2x+3*2x-2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

24x^2+4x-2=0

a = 24; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·24·(-2)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*24}=\frac{-4-4\sqrt{13}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*24}=\frac{-4+4\sqrt{13}}{48}
$