9/2y-12=1/4y-4

Solution for 9/2y-12=1/4y-4 equation:

9/2y-12=1/4y-4

We move all terms to the left:

9/2y-12-(1/4y-4)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

9/2y-1/4y+4-12=0

We calculate fractions


36y/8y^2+(-2y)/8y^2+4-12=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-64y^2+36y+(-2y)=0

We get rid of parentheses

-64y^2+36y-2y=0

We add all the numbers together, and all the variables

-64y^2+34y=0

a = -64; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-64)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-64}=\frac{-68}{-128}
=17/32
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-64}=\frac{0}{-128}
=0
$