(3)/(4)y-(5)/(6)=(2)/(3)y

Solution for (3)/(4)y-(5)/(6)=(2)/(3)y equation:

(3)/(4)y-(5)/(6)=(2)/(3)y

We move all terms to the left:

(3)/(4)y-(5)/(6)-((2)/(3)y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y-(+2/3y)-5/6=0

We get rid of parentheses

3/4y-2/3y-5/6=0

We calculate fractions


(-180y^2)/432y^2+324y/432y^2+(-288y)/432y^2=0

We multiply all the terms by the denominator


(-180y^2)+324y+(-288y)=0

We get rid of parentheses

-180y^2+324y-288y=0

We add all the numbers together, and all the variables

-180y^2+36y=0

a = -180; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-180)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-180}=\frac{-72}{-360}
=1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-180}=\frac{0}{-360}
=0
$