1/6y-1/2=3-1/2y

Solution for 1/6y-1/2=3-1/2y equation:

1/6y-1/2=3-1/2y

We move all terms to the left:

1/6y-1/2-(3-1/2y)=0


Domain of the equation: 6y!=0

y!=0/6

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

1/6y-(-1/2y+3)-1/2=0

We get rid of parentheses

1/6y+1/2y-3-1/2=0

We calculate fractions


8y/48y^2+6y/48y^2+(-6y)/48y^2-3=0

We multiply all the terms by the denominator


8y+6y+(-6y)-3*48y^2=0

We add all the numbers together, and all the variables

14y+(-6y)-3*48y^2=0

Wy multiply elements

-144y^2+14y+(-6y)=0

We get rid of parentheses

-144y^2+14y-6y=0

We add all the numbers together, and all the variables

-144y^2+8y=0

a = -144; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-144)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-144}=\frac{-16}{-288}
=1/18
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-144}=\frac{0}{-288}
=0
$