1/3y+1/6y=9/5

Solution for 1/3y+1/6y=9/5 equation:

1/3y+1/6y=9/5

We move all terms to the left:

1/3y+1/6y-(9/5)=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

1/3y+1/6y-(+9/5)=0

We get rid of parentheses

1/3y+1/6y-9/5=0

We calculate fractions


(-972y^2)/450y^2+150y/450y^2+75y/450y^2=0

We multiply all the terms by the denominator


(-972y^2)+150y+75y=0

We add all the numbers together, and all the variables

(-972y^2)+225y=0

We get rid of parentheses

-972y^2+225y=0

a = -972; b = 225; c = 0;
Δ = b2-4ac
Δ = 2252-4·(-972)·0
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-225}{2*-972}=\frac{-450}{-1944}
=25/108
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+225}{2*-972}=\frac{0}{-1944}
=0
$