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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y+1)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


3y/6y^2+(-4y)/6y^2-1-4=0

We add all the numbers together, and all the variables

3y/6y^2+(-4y)/6y^2-5=0

We multiply all the terms by the denominator


3y+(-4y)-5*6y^2=0

Wy multiply elements

-30y^2+3y+(-4y)=0

We get rid of parentheses

-30y^2+3y-4y=0

We add all the numbers together, and all the variables

-30y^2-1y=0

a = -30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-30}=\frac{0}{-60}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-30}=\frac{2}{-60}
=-1/30
$