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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 2y-4)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


18y/8y^2+(-4y)/8y^2+4-12=0

We add all the numbers together, and all the variables

18y/8y^2+(-4y)/8y^2-8=0

We multiply all the terms by the denominator


18y+(-4y)-8*8y^2=0

Wy multiply elements

-64y^2+18y+(-4y)=0

We get rid of parentheses

-64y^2+18y-4y=0

We add all the numbers together, and all the variables

-64y^2+14y=0

a = -64; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-64)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-64}=\frac{-28}{-128}
=7/32
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-64}=\frac{0}{-128}
=0
$