1/2y+1/6y=6/7

Solution for 1/2y+1/6y=6/7 equation:

1/2y+1/6y=6/7

We move all terms to the left:

1/2y+1/6y-(6/7)=0


Domain of the equation: 2y!=0

y!=0/2

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

1/2y+1/6y-(+6/7)=0

We get rid of parentheses

1/2y+1/6y-6/7=0

We calculate fractions


(-432y^2)/588y^2+294y/588y^2+98y/588y^2=0

We multiply all the terms by the denominator


(-432y^2)+294y+98y=0

We add all the numbers together, and all the variables

(-432y^2)+392y=0

We get rid of parentheses

-432y^2+392y=0

a = -432; b = 392; c = 0;
Δ = b2-4ac
Δ = 3922-4·(-432)·0
Δ = 153664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{153664}=392$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(392)-392}{2*-432}=\frac{-784}{-864}
=49/54
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(392)+392}{2*-432}=\frac{0}{-864}
=0
$