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

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

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

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



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

y∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

36y/4y^2+(-1y)/4y^2+4-12=0

We add all the numbers together, and all the variables

36y/4y^2+(-1y)/4y^2-8=0

We multiply all the terms by the denominator


36y+(-1y)-8*4y^2=0

Wy multiply elements

-32y^2+36y+(-1y)=0

We get rid of parentheses

-32y^2+36y-1y=0

We add all the numbers together, and all the variables

-32y^2+35y=0

a = -32; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-32)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-32}=\frac{-70}{-64}
=1+3/32
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-32}=\frac{0}{-64}
=0
$