3/4y-5/6=7/12y

Solution for 3/4y-5/6=7/12y equation:

3/4y-5/6=7/12y

We move all terms to the left:

3/4y-5/6-(7/12y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 12y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y-(+7/12y)-5/6=0

We get rid of parentheses

3/4y-7/12y-5/6=0

We calculate fractions


(-240y^2)/1728y^2+1296y/1728y^2+(-1008y)/1728y^2=0

We multiply all the terms by the denominator


(-240y^2)+1296y+(-1008y)=0

We get rid of parentheses

-240y^2+1296y-1008y=0

We add all the numbers together, and all the variables

-240y^2+288y=0

a = -240; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·(-240)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*-240}=\frac{-576}{-480}
=1+1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*-240}=\frac{0}{-480}
=0
$