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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



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

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

1y*4y-12*4y+8=0

Wy multiply elements

4y^2-48y+8=0

a = 4; b = -48; c = +8;
Δ = b2-4ac
Δ = -482-4·4·8
Δ = 2176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{34}}{2*4}=\frac{48-8\sqrt{34}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{34}}{2*4}=\frac{48+8\sqrt{34}}{8}
$