6-4/3y=14-5/4y

Solution for 6-4/3y=14-5/4y equation:

6-4/3y=14-5/4y

We move all terms to the left:

6-4/3y-(14-5/4y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-4/3y-(-5/4y+14)+6=0

We get rid of parentheses

-4/3y+5/4y-14+6=0

We calculate fractions


(-16y)/12y^2+15y/12y^2-14+6=0

We add all the numbers together, and all the variables

(-16y)/12y^2+15y/12y^2-8=0

We multiply all the terms by the denominator


(-16y)+15y-8*12y^2=0

We add all the numbers together, and all the variables

15y+(-16y)-8*12y^2=0

Wy multiply elements

-96y^2+15y+(-16y)=0

We get rid of parentheses

-96y^2+15y-16y=0

We add all the numbers together, and all the variables

-96y^2-1y=0

a = -96; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-96)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-96}=\frac{0}{-192}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-96}=\frac{2}{-192}
=-1/96
$