1/4y=2/3y-1

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

1/4y=2/3y-1

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



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

y∈R


We get rid of parentheses

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

We calculate fractions


3y/12y^2+(-8y)/12y^2+1=0

We multiply all the terms by the denominator


3y+(-8y)+1*12y^2=0

Wy multiply elements

12y^2+3y+(-8y)=0

We get rid of parentheses

12y^2+3y-8y=0

We add all the numbers together, and all the variables

12y^2-5y=0

a = 12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·12·0
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*12}=\frac{0}{24}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*12}=\frac{10}{24}
=5/12
$