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

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

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

We move all terms to the left:

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


Domain of the equation: 3y+4)!=0

y∈R



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

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

3y+1y)!=3

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-y*3y+4*3y+3*3y-1*3y-5=0

Wy multiply elements

-3y^2+12y+9y-3y-5=0

We add all the numbers together, and all the variables

-3y^2+18y-5=0

a = -3; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·(-3)·(-5)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{66}}{2*-3}=\frac{-18-2\sqrt{66}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{66}}{2*-3}=\frac{-18+2\sqrt{66}}{-6}
$