(4x-2)/(6-3x)=6-2x

Solution for (4x-2)/(6-3x)=6-2x equation:

(4x-2)/(6-3x)=6-2x

We move all terms to the left:

(4x-2)/(6-3x)-(6-2x)=0


Domain of the equation: (6-3x)!=0

We move all terms containing x to the left, all other terms to the right

-3x!=-6

x!=-6/-3

x!=+2

x∈R


We add all the numbers together, and all the variables

(4x-2)/(-3x+6)-(-2x+6)=0

We get rid of parentheses

(4x-2)/(-3x+6)+2x-6=0

We multiply all the terms by the denominator


(4x-2)+2x*(-3x+6)-6*(-3x+6)=0

We multiply parentheses

-6x^2+(4x-2)+12x+18x-36=0

We get rid of parentheses

-6x^2+4x+12x+18x-2-36=0

We add all the numbers together, and all the variables

-6x^2+34x-38=0

a = -6; b = 34; c = -38;
Δ = b2-4ac
Δ = 342-4·(-6)·(-38)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{61}}{2*-6}=\frac{-34-2\sqrt{61}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{61}}{2*-6}=\frac{-34+2\sqrt{61}}{-12}
$