X-2=2/3y

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

X-2=2/3X

We move all terms to the left:

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


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

X-2/3X-2=0

We multiply all the terms by the denominator


X*3X-2*3X-2=0

Wy multiply elements

3X^2-6X-2=0

a = 3; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·3·(-2)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*3}=\frac{6-2\sqrt{15}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*3}=\frac{6+2\sqrt{15}}{6}
$