1/4y-5=1/6y

Solution for 1/4y-5=1/6y equation:

1/4y-5=1/6y

We move all terms to the left:

1/4y-5-(1/6y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/4y-(+1/6y)-5=0

We get rid of parentheses

1/4y-1/6y-5=0

We calculate fractions


6y/24y^2+(-4y)/24y^2-5=0

We multiply all the terms by the denominator


6y+(-4y)-5*24y^2=0

Wy multiply elements

-120y^2+6y+(-4y)=0

We get rid of parentheses

-120y^2+6y-4y=0

We add all the numbers together, and all the variables

-120y^2+2y=0

a = -120; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-120)·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*-120}=\frac{-4}{-240}
=1/60
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-120}=\frac{0}{-240}
=0
$