1/3y+4=17-1/6y

Solution for 1/3y+4=17-1/6y equation:

1/3y+4=17-1/6y

We move all terms to the left:

1/3y+4-(17-1/6y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(-1/6y+17)+4=0

We get rid of parentheses

1/3y+1/6y-17+4=0

We calculate fractions


6y/18y^2+3y/18y^2-17+4=0

We add all the numbers together, and all the variables

6y/18y^2+3y/18y^2-13=0

We multiply all the terms by the denominator


6y+3y-13*18y^2=0

We add all the numbers together, and all the variables

9y-13*18y^2=0

Wy multiply elements

-234y^2+9y=0

a = -234; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-234)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-234}=\frac{-18}{-468}
=1/26
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-234}=\frac{0}{-468}
=0
$