1/4y-5=1/9y

Solution for 1/4y-5=1/9y equation:

1/4y-5=1/9y

We move all terms to the left:

1/4y-5-(1/9y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 9y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/4y-(+1/9y)-5=0

We get rid of parentheses

1/4y-1/9y-5=0

We calculate fractions


9y/36y^2+(-4y)/36y^2-5=0

We multiply all the terms by the denominator


9y+(-4y)-5*36y^2=0

Wy multiply elements

-180y^2+9y+(-4y)=0

We get rid of parentheses

-180y^2+9y-4y=0

We add all the numbers together, and all the variables

-180y^2+5y=0

a = -180; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-180)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-180}=\frac{-10}{-360}
=1/36
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-180}=\frac{0}{-360}
=0
$