5/6y-2/3y=3/8

Solution for 5/6y-2/3y=3/8 equation:

5/6y-2/3y=3/8

We move all terms to the left:

5/6y-2/3y-(3/8)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

5/6y-2/3y-(+3/8)=0

We get rid of parentheses

5/6y-2/3y-3/8=0

We calculate fractions


(-162y^2)/1152y^2+960y/1152y^2+(-768y)/1152y^2=0

We multiply all the terms by the denominator


(-162y^2)+960y+(-768y)=0

We get rid of parentheses

-162y^2+960y-768y=0

We add all the numbers together, and all the variables

-162y^2+192y=0

a = -162; b = 192; c = 0;
Δ = b2-4ac
Δ = 1922-4·(-162)·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-192}{2*-162}=\frac{-384}{-324}
=1+5/27
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+192}{2*-162}=\frac{0}{-324}
=0
$