1/y-2-1/2=-2y/4y-1

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

1/y-2-1/2=-2y/4y-1

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



Domain of the equation: 4y-1)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


(-16y^2)/16y^2+8y^2/16y^2+16y/16y^2+1-2=0

We add all the numbers together, and all the variables

(-16y^2)/16y^2+8y^2/16y^2+16y/16y^2-1=0

We multiply all the terms by the denominator


(-16y^2)+8y^2+16y-1*16y^2=0

We add all the numbers together, and all the variables

8y^2+(-16y^2)+16y-1*16y^2=0

Wy multiply elements

8y^2+(-16y^2)-16y^2+16y=0

We get rid of parentheses

8y^2-16y^2-16y^2+16y=0

We add all the numbers together, and all the variables

-24y^2+16y=0

a = -24; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-24)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-24}=\frac{-32}{-48}
=2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-24}=\frac{0}{-48}
=0
$