1/6y+1/3y=3/10

Solution for 1/6y+1/3y=3/10 equation:

1/6y+1/3y=3/10

We move all terms to the left:

1/6y+1/3y-(3/10)=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

1/6y+1/3y-(+3/10)=0

We get rid of parentheses

1/6y+1/3y-3/10=0

We calculate fractions


(-162y^2)/180y^2+30y/180y^2+60y/180y^2=0

We multiply all the terms by the denominator


(-162y^2)+30y+60y=0

We add all the numbers together, and all the variables

(-162y^2)+90y=0

We get rid of parentheses

-162y^2+90y=0

a = -162; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-162)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-162}=\frac{-180}{-324}
=5/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-162}=\frac{0}{-324}
=0
$