4/9y-12=4/1y-4

Solution for 4/9y-12=4/1y-4 equation:

4/9y-12=4/1y-4

We move all terms to the left:

4/9y-12-(4/1y-4)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



Domain of the equation: 1y-4)!=0

y∈R


We get rid of parentheses

4/9y-4/1y+4-12=0

We calculate fractions


4y/9y^2+(-36y)/9y^2+4-12=0

We add all the numbers together, and all the variables

4y/9y^2+(-36y)/9y^2-8=0

We multiply all the terms by the denominator


4y+(-36y)-8*9y^2=0

Wy multiply elements

-72y^2+4y+(-36y)=0

We get rid of parentheses

-72y^2+4y-36y=0

We add all the numbers together, and all the variables

-72y^2-32y=0

a = -72; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-72)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-72}=\frac{0}{-144}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-72}=\frac{64}{-144}
=-4/9
$