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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2y/8y^2+4y/8y^2-2-1=0

We add all the numbers together, and all the variables

2y/8y^2+4y/8y^2-3=0

We multiply all the terms by the denominator


2y+4y-3*8y^2=0

We add all the numbers together, and all the variables

6y-3*8y^2=0

Wy multiply elements

-24y^2+6y=0

a = -24; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-24)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-24}=\frac{-12}{-48}
=1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-24}=\frac{0}{-48}
=0
$