3/4y-5=-1+1/3y

Solution for 3/4y-5=-1+1/3y equation:

3/4y-5=-1+1/3y

We move all terms to the left:

3/4y-5-(-1+1/3y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y-(1/3y-1)-5=0

We get rid of parentheses

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

We calculate fractions


9y/12y^2+(-4y)/12y^2+1-5=0

We add all the numbers together, and all the variables

9y/12y^2+(-4y)/12y^2-4=0

We multiply all the terms by the denominator


9y+(-4y)-4*12y^2=0

Wy multiply elements

-48y^2+9y+(-4y)=0

We get rid of parentheses

-48y^2+9y-4y=0

We add all the numbers together, and all the variables

-48y^2+5y=0

a = -48; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-48)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-48}=\frac{-10}{-96}
=5/48
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-48}=\frac{0}{-96}
=0
$