(-4/3y+1)+2=y

Solution for (-4/3y+1)+2=y equation:

(-4/3y+1)+2=y

We move all terms to the left:

(-4/3y+1)+2-(y)=0


Domain of the equation: 3y+1)!=0

y∈R


We add all the numbers together, and all the variables

-1y+(-4/3y+1)+2=0

We get rid of parentheses

-1y-4/3y+1+2=0

We multiply all the terms by the denominator


-1y*3y+1*3y+2*3y-4=0

Wy multiply elements

-3y^2+3y+6y-4=0

We add all the numbers together, and all the variables

-3y^2+9y-4=0

a = -3; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·(-3)·(-4)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{33}}{2*-3}=\frac{-9-\sqrt{33}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{33}}{2*-3}=\frac{-9+\sqrt{33}}{-6}
$