3y/4y-1=1/y

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

3y/4y-1=1/y

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


3y^2+(-4y)-1*4y^2=0

Wy multiply elements

3y^2-4y^2+(-4y)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1y^2-4y=0

a = -1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-1}=\frac{0}{-2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1}=\frac{8}{-2}
=-4
$