1/4y+3=1/2y

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

1/4y+3=1/2y

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

24y^2+2y+(-4y)=0

We get rid of parentheses

24y^2+2y-4y=0

We add all the numbers together, and all the variables

24y^2-2y=0

a = 24; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·24·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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