Y-x=2x-2/3x

Solution for Y-x=2x-2/3x equation:

-Y=2Y-2/3Y

We move all terms to the left:

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


Domain of the equation: 3Y)!=0

Y!=0/1

Y!=0

Y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1Y-(+2Y-2/3Y)=0

We get rid of parentheses

-1Y-2Y+2/3Y=0

We multiply all the terms by the denominator


-1Y*3Y-2Y*3Y+2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-9Y^2+2=0

a = -9; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-9)·2
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-9}=\frac{0-6\sqrt{2}}{-18}
=-\frac{6\sqrt{2}}{-18}
=-\frac{\sqrt{2}}{-3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-9}=\frac{0+6\sqrt{2}}{-18}
=\frac{6\sqrt{2}}{-18}
=\frac{\sqrt{2}}{-3}
$