2/3y+1/6y=5/2

Solution for 2/3y+1/6y=5/2 equation:

2/3y+1/6y=5/2

We move all terms to the left:

2/3y+1/6y-(5/2)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y+1/6y-(+5/2)=0

We get rid of parentheses

2/3y+1/6y-5/2=0

We calculate fractions


(-540y^2)/72y^2+48y/72y^2+12y/72y^2=0

We multiply all the terms by the denominator


(-540y^2)+48y+12y=0

We add all the numbers together, and all the variables

(-540y^2)+60y=0

We get rid of parentheses

-540y^2+60y=0

a = -540; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-540)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-540}=\frac{-120}{-1080}
=1/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-540}=\frac{0}{-1080}
=0
$