X=2y-6/3y-2

Solution for X=2y-6/3y-2 equation:

X=2X-6/3X-2

We move all terms to the left:

X-(2X-6/3X-2)=0


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

X∈R


We get rid of parentheses

X-2X+6/3X+2=0

We multiply all the terms by the denominator


X*3X-2X*3X+2*3X+6=0

Wy multiply elements

3X^2-6X^2+6X+6=0

We add all the numbers together, and all the variables

-3X^2+6X+6=0

a = -3; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-3)·6
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*-3}=\frac{-6-6\sqrt{3}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*-3}=\frac{-6+6\sqrt{3}}{-6}
$